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88070872 


88 


Report No. 


UNITED STATES 
DEPARTMENT OF THE INTERIOR 

BUREAU OF MINES 
HELIUM ACTIVITY 
HELIUM RESEARCH CENTER 

INTERNAL REPORT 


COMPRESSIBILITY DATA FOR HELIUM AT 0° C AND 


PRESSURES TO 800 ATMOSPHERES 



Ted C. Briggs 


BRANCH 


Fundamental Research 



9660 
. H43 
M56 
no. 88 


PROJECT NO. _m_ 

QATE _ March 1966 


AMARILLO, TEXAS 
























O 


,h43 

M% 

no.^6 

Report No. 88 


HELIUM RESEARCH CENTER 
INTERNAL REPORT 


COMPRESSIBILITY DATA FOR HELIUM AT 0° C AND 
PRESSURES TO 800 ATMOSPHERES 


By 


Ted C. Briggs 


Branch of Fundamental Research 
Project 4330 
March 1966 


BLM Library 
Denver Federal Center 
Bldg. 50, OC-521 
P.O. Box 25047 
Denver, CO 80225 































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CONTENTS 


Abstract . . 

Introduction ..••■••••••••••• 

Experimental apparatus . ... 

Experimental procedure . ... 

Calculation of corrected pressures from the 
experimental observations. ... . 

Composition of the test gas. 

Compressibility-bomb bath temperatures . . . 

Calculation of constants and compressibility 
factors from the observed pressures. . . . 

Discussion of results. 

References . 


Page 

4 

4 

5 

21 

, 24 
. 29 
. 32 

. 32 
. 109 
. 110 


ILLUSTRATIONS 


Figj- „ , 

1. Gas pressure system of the high-pressure 

compressibility apparatus. . . . 

2. Oil pressure system of the high-pressure 

compressibility apparatus. 

3. Constant temperature bath system and some of 

the major components of the high-pressure 
compressibility apparatus. . . . 









































f 

















































































3 


TABLES 


1 . 

2 . 

3. 

4. 

5. 

6 . 

7 . 

8 . 

9. 

10 . 

11 . 


Page 

Compressibility apparatus valv.es. 

Analysis of vent samples, parts per million 

by volume impurities in belium . 

Helium cylinder analysis, parts per million 

by volume impurities in helium . ^ 

Compressibility-bomb bath temperatures . 33 

Experimental pressures, calculated pressures, constants, 

standard errors, variances, and covariances.37 


Variances and covariances at even increments 

of pressure. 

Compressibility factors and standard errors at 

even increments of pressure. . . 

Compressibility apparatus zero pressure volume ratio 

Values for the constant B at 0° C.. 

Values for the constant C at 0° C. 

Compressibility factor for helium at 0° C and 

1 atmosphere ..... . 

Compressibility factor for helium at 0° C and 

700 atmospheres.-. 


. 39 

. 81 
.103 
.105 
.106 

.107 

.108 


12 . 




































































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4 


COMPRESSIBILITY DATA FOR HELIUM AT 0° C AND 
PRESSURES TO 800 ATMOSPHERES 

by 

Ted C. Briggs^ 

ABSTRACT 

Twenty - two compressibility runs were made with helium at 0 C. 

The apparatus used to obtain the data is described. The experi¬ 
mental procedure is described. The method used to calculate a 
corrected pressure from the experimental observations is discussed 
in detail. The data were fitted to an equation of the form 

O 

Z = 1 + BP + CP and the results are presented, 
r r r 

INTRODUCTION 

Numerous compressibility runs were made with helium at 0 C 
starting at approximately the same initial pressure. The purpose of 
making multiple runs at one temperature was to test the statistical 
agreement between runs, to test a functional form for representing 
the data, and to ultimately present precise new data for the compres¬ 
sibility factors of helium at 0° C. 

1/ Research chemist. Helium Research Center, Bureau of Mines, 
Amarillo, Texas. 


Work on manuscript completed March 1966. 





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5 


EXPERIMENTAL APPARATUS 


The experimental apparatus used to obtain the data of this re- 

27 

port was a conventional Burnett (9}~ type compressibility apparatus. 


2 J Underlined numbers in parentheses refer to items in the list of 
references at the end of this report. 


The original Burnett compressibility apparatus consisted of two vol¬ 
umes designated as and , equipment to control and measure the 
temperature of and , and equipment to measure the pressure of 
a gas sample confined in the volume or The compressibility 

apparatus used in this investigation was quite similar to Burnett's 
original apparatus. Burnett's original apparatus had a volume ratio 


/VI 

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of approximately two as did the apparatus used in this invest 


tigation. The original Burnett apparatus had oil jackets around the 
gas pressure bombs. Burnett's apparatus was arranged to have oil 
pressure in the jackets equal the gas pressure confined in the bombs. 
For a thick wall cylinder, this arrangement reduced, but did not 
eliminate elastic pressure distortion of the compressibility bombs. 
The present compressibility apparatus also had oil jackets around the 
gas bombs; however, the oil jacket-pressure system was separate from 
the oil pressure system of the piston gage. The oil jackets of the 
present compressibility apparatus were used to help determine pres¬ 
sure distortion coefficients as reported in references (4), (5 ), (6}, 
and (_7) . The oil jackets were not used during any of the compressi¬ 
bility runs of this report. 





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The compressibility bombs used in this investigation were fab¬ 
ricated in the Amarillo Helium Plant machine shop. All other major 
equipment items incorporated in the present compressibility apparatus 
were commercially available. 

Dimensions of the jacketed bombs, a description of the components 

of and ; and an estimate of the volumes of and were re- 

3 / 

corded in reference (5.) — . All of the components constituting. and 

3/ The high-pressure jacketed bombs used in this investigation were 
designed by John E. Miller, Research Chemist, Helium Research 
Center, Bureau of Mines, Amarillo, Texas. The dimensions of the 
jacketed bomb illustrated in reference (j>) , figure 1, page 6, 
were supplied to this writer by John E. Miller. 


were assembled in a constant temperature bath; therefore, all of 
the gas sample confined in volume or was at the bath tempera¬ 

ture . 

The constant temperature bath used in this investigation was a 

4 / 

Chandler Engineering Company— Model No. 22-1 bath assembly. The 


4/ Manufacturers were identified in this report for descriptive 
purposes only, and this identification should not be construed 
as endorsement or recommendation of any particular product or 
manufacturer. 


bath was supplied with a 1,000 watt immersion heater, a 500 watt 





















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immersion heater controlled by a variable transformer, and a 100 watt 
immersion heater. The bath was supplied equipped with heat exchange 
coils of 1/4" od copper tubing through which various fluids could 
be circulated. Refrigeration was supplied to the compressibility 
bath by pumping fluid through the heat exchange coils from an exter¬ 
nal tank. The external tank contained a 750 watt immersion heater, 
a 500 watt immersion heater controlled by a variable transformer, a 
100 watt immersion heater, and the refrigeration coils of a Tecumseh 
Model No. C2513HTK refrigeration unit. The refrigeration unit was 
controlled by a relay system actuated by a mercury thermoregulator. 
Temperature of the fluid in the external tank was controlled within 
about + 0.03° C of the set temperature by the on-off action of the 
Tecumseh refrigeration unit. Fluid was pumped from the external 
tank through the heat exchange coils of the compressibility bath 
by a Viking Model No. F656G positive displacement pump with a built- 
in relief valve. There was a pressure drop of about 50 psi through 
the heat exchange coils. Fine temperature control of the compressi¬ 
bility bath was obtained by supplying a small amount of extra refrige¬ 
ration to the bath and controlling the temperature with the 100 watt 
immersion heater. Power to the 100 watt immersion heater was 
supplied through a Hallikainen Thermotrol temperature controller with 
a Model No. 1080 temperature-sensing element. The controller was 
actuated by a + 0.001° C change in the bath temperature. The 
Hallikainen temperature controller was of the proportional with 
reset type; therefore, the controller supplied only enough power to 
the 100 watt heater to maintain the set temperature, and avoided the 


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8 


temperature fluctuations experienced with on-off type controllers. 

The compressibility bath was filled with a ten percent by 
volume methyl alcohol in water antifreeze mixture for the 0° C com¬ 
pressibility runs. The bath was stirred by an internal circulating 
pump and by a 1/30 h.p. Aminco electrical stirrer. A fifty percent 
by volume ethylene glycol in water antifreeze mixture was circulated 
from the external tank through the compressibility bath heat exchange 
coils. 

Compressibility bath temperatures were measured with a Leeds & 
Northrup Model No. 8163, Serial No. 1586182 platinum resistance 
thermometer. The thermometer was calibrated by the company at the 
ice point, steam point, boiling point of sulphur, and boiling point 
of oxygen. Constants were supplied by the company for use in the 
Callendar and modified Callendar temperature interpolation formulas. 
Temperatures measured with the platinum resistance thermometer were 
in terms of the International Practical Temperature Scale. The 
manufacturer stated that the calibrated thermometer would reproduce 
temperatures on the International Practical Temperature Scale within 
+ 0.01° C provided the thermometer was used with a calibrated resis¬ 
tance bridge and provided a reliable value was used for the resis¬ 
tance of the thermometer at the ice point. A value for the ice 
point resistance of platinum resistance thermometer, Serial No. 
.1586182, was determined in this laboratory (2) . Thermometer resis¬ 
tances were measured with a Leeds A Northrup Company Model No. 8069 
G-2 Mueller bridge, Serial No. 1603629. A constant current of 2 


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9 


milliamperes was supplied to the thermometer for all resistance 
measurements. The G-2 Mueller bridge was calibrated by the manu¬ 
facturer and corrections were provided with sufficient precision to 
determine a resistance or change of resistance greater than 1 ohm 
to about 2 parts in 100,000. The Model No. 8069 bridge could mea¬ 
sure resistances over the range 0 to 111.111 ohms. ihe smallest 
decade step was 0.0001 ohm. A temperature change of 0,001° C 
changed the resistance of the platinum resistance thermometer by 
about 0.0001 ohm at 0° C. The G-2 Mueller bridge was supplied 
equipped with a mercury contact commutator for reversing the 
connections to the four lead platinum resistance thermometer for 
the purpose of cancelling the effect of thermometer lead resistance. 
Critical resistance coils of the Model No. 8069 bridge were mounted 
in a thermally insulated block whose temperature was kept constant 
by means of an electrical heater controlled by a thermoregulator. 

This arrangement eliminated the need to make temperature corrections 
to the bridge resistance readings. A Keithley Instruments, Inc. 
Model No. 149 electronic milli-microvoltmeter was used as a null- 
detector for the G-2 Mueller bridge. The milli-microvoltmeter had 
a range of measurements from 0.1 microvolt full scale to 100 milli¬ 
volts. One minor irritation experienced with the null-detector was 
that everytime the Mueller bridge thermoregulator came on, the null- 
detector would go off scale; therefore, all thermometer resistance 
measurements were made when the bridge thermoregulator was off. The 
null-detector also seemed rather sensitive to line voltage distur¬ 
bances; however, the electronic null-detector eliminated many of the 





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10 


problems associated with the use of a moving-coil galvanometer. 

Gas samples in the compressibility bombs were separated from 
oil of the pressure-measuring system by a Ruska Instrument Corpo 
ration Model No. 2416, Serial No. 9032 differential pressure cell. 
The differential pressure cell used in this investigation was 
modified by the manufacturer so the cell could be immersed in the 
compressibility bath fluid. The cell was designed to safely with¬ 
stand an overpressure of 15,000 psi on either side of the diaphragm. 
Oil of the pressure-measuring system was separated from gas of the 
sample system by a thin stainless steel diaphragm located within 
the cell. The position of the diaphragm was established by the 
movement of a stem soldered to the diaphragm. As the diaphragm 
moved, the stem moved a core within the coils of a very sensitive 
differential transformer. Output of the differential transformer 
was indicated by an electronic meter. The maximum sensitivity of 
the differential pressure cell and meter was about 0.0001 psi. The 
differential pressure cell meter was zeroed before each run with 
atmospheric pressure applied to both sides of the diaphragm. The 
zero of the differential pressure changed with increasing operating 
pressure due to pressure distortion of the cell. Ruska Instrument 
Corporation provided the calibration data necessary to correct for 
a change of the cell zero due to a change of the cell operating 
pressure. Large overpressures were avoided on either side of the 
diaphragm in order to prevent a change of the cell zero during a 
compressibility run. It was not possible to apply a numerical 









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11 


correction for zero shift due to overpressures; therefore, large 
overpressures were not applied to either side of the diaphragm 
during a run, and any small overpressures were applied consistently 
to the ofl side of the diaphragm. Gas pressures on the sample side 
of the diaphragm were balanced on the oil side of the diaphragm by 
an oil lubricated dead weight piston gage. The piston gage used in 
this investigation was a Ruska Instrument Corporation Model No. 2400 
gage, Serial No. 9274. The gage was calibrated by the manufacturer 
by comparison against Ruska Instrument Corporation master gage 
Serial No. 7544. The area of the master gage was determined at the 
National Bureau of Standards and was reported to be correct to one 
part in 10,000 at 25° C. The comparison of gage No. 9274 against the 
master gage was carried out with a precision of a few parts per 
million; therefore, the calibration accuracy of gage Serial No. 9274 
should be essentially the same as the accuracy of the master gage. 

Ruska Instrument Corporation supplied calibration data for the indi¬ 
vidual piston gage weights, a value for the piston gage area at 25° C, 
a coefficient to correct for a change of piston gage area as a function 
of pressure, and a coefficient to correct for change of gage tempera¬ 
ture from the calibration temperature. The range of the gage used 
in this investigation was from 30 to 12,140 psig. The minimum reso¬ 
lution of the gage was stated by the manufacturer to be 5 parts per 
million at full load decreasing to 50 parts per million at empty 
weight. The height of the piston gage reference plane was adjusted, 
by placing brass blocks under the piston gage legs, to correspond to 
the level of the diaphragm of the differential pressure cell and to 






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12 


the zero of the oil manometer; therefore, the necessity of making 
oil head pressure corrections was eliminated. The pressure bombs 
were placed horizontally in the bomb bath. The center of the 
jacketed bomb portion of was about 7.0 cm below the level of 
the diaphragm and the center of the jacketed bomb portion of 
was about 10.2 cm below the level of the diaphragm. Pressure in 
the oil system was adjusted by use of a Ruska Instrument Corpora¬ 
tion oil displacement pump. A Ruska Instrument Corporation Model 
No. 2409 oil manometer was located in the oil system. The zero of 
the oil manometer was adjusted to correspond to the level of the 
diaphragm of the differential pressure cell. 

Barometric pressures were measured with a Henry J. Green 
Instruments, Inc. Model No. 16, Serial No. 13346 Fortin type mercur¬ 
ial barometer. The barometer was calibrated at the National Bureau 
of Standards. All barometer readings for the data of this report 
were made to the nearest 0.05 millimeter of mercury. Reduction of 
observed barometer readings to standard conditions has been dis¬ 
cussed in Helium Research Center Internal Report 68 (_3) . 

Relative humidity in the PVT laboratory was measured with a 
sensitive hygrometer manufactured by Bacharach Industrial Instrument 
Company. The manufacturer stated an accuracy of + 1.5 percent rela¬ 
tive humidity for the hygrometer. 

Volume V 2 of the PVT apparatus was evacuated by a Welch Scienti 
fic Company Model No. 1400B high-vacuum pump. The manufacturer 
claimed an ultimate vacuum capability of 0.1 micron for the Model No 


1400B vacuum pump. 















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13 


The degree of vacuum in was measured with a Consolidated 

Vacuum Corporation Model No. GPH-100A vacuum gage with a No. 

GPH-001 cold cathode ionization tube. The vacuum gage was designed 

-7 -3 

to measure pressures over the range 1 x 10 to 25 x 10 millimeters 
of mercury. The actual degree of vacuum attained in volume of 
the compressibility apparatus, as indicated by the vacuum gage, 
ranged between ten and five microns. 

The compressibility bombs were filled with gas by use of a 
Corblin Model No. B2C 1000 diaphragm type compressor. The compres¬ 
sor was designed for use to 15,000 psi, and had a compression ratio 
of twenty to one. 

An unsealed diagram of the gas pressure system of the compres¬ 
sibility apparatus is included in this report ss figure 1. An 
unsealed diagram of the oil pressure system is illustrated in 
figure 2. An unsealed illustration of the constant temperature bath 
system along with some of the major components of the compressibility 
apparatus is included in this report as figure 3. and V fe2 of 

figures 1, 2, and 3 illustrate the jacketed bomb portions of V 1 and 
V . Figures 1, 2, and 3 are not intended to show minute details of 
the compressibility apparatus, but are intended to illustrate the 
general arrangement of most of the major components of the compres¬ 
sibility apparatus. The valves of the compressibility apparatus are 
numbered in figures 1 and 2 and the valve functions are listed in 


table 1. 


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High -pressure 
gage 



FIGURE I. - Gas Pressure System of the High - Pressure 
Compressibility Apparatus. 
















































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15 



Oil Displacement Pump 
No 2 


Oil manometer 


Piston gage 



Differential 

Pressure 

Cell 


High-pressure gage 


Oil 

reservoir 


Oil Displacement Pump 
No I 


FIGURE 2.-Oil Pressure System of the High-Pressure 

Compressibility Apparatus. 















































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Differential 
Pressure 
Cell Meter 



Platimum 

resistance 

thermometer 


Refrigerator 


HGURE 3 —'"onstonf Temperature Bath System and Some of the Major 
‘ omponents of the High — Pressure Compressibility Apparatus. 






























































































































































































































17 


TABLE 1. - Compressibility apparatus valves 
Valve No. Function 

1 Inlet valve to the Corblin gas compressor from the 

gas supply cylinder. Valve was open when filling 
the gas system and when operating the compressor. 
Valve was closed at all other times. 


2 


3 


4 


5 


High-pressure gas outlet valve to room 107A. Valve 
was closed at all times during all steps of a com¬ 
pressibility run. 

High-pressure gas vent valve to outside of Building 
A. Purpose of the valve was to provide a means of 
rapidly venting gas from the compressor lines in case 
of emergency. Valve was closed at all times during 
a routine compressibility run. 

Inlet valve to the compressibility bombs. Valve 
was open during evacuation of the compressor lines, 
during purging of the system with test gas, during 
filling of the compressibility bombs, and when gas 
was vented from the compressor lines during routine 
operation. Valve was closed at all other times. 

Expansion valve separating volumes V^ and V^• Valve 
was open when evacuating V^, when filling V^ with 
test gas, and when expanding gas from V^ to V^. 

Valve was closed at all other times. 







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18 


TABLE 1. - Compressibility apparatus valves (Con.) 

Valve No. Function 

6 High-pressure exhaust valve from the compressibility 

bombs. Valve was open when evacuating V^, V^, or 
the compressor lines. Valve was open when venting 
gas from V^, V , or the compressor lines during rou¬ 
tine operation. Valve was closed at all other times. 


7 Low-pressure (3,000 psi) valve to vent line to out¬ 
side of Building A. Valve was FULL OPEN WHEN VENTING 
HIGH-PRESSURE GAS THROUGH VALVE 6. Failure to open 
valve 7 when venting high-pressure gas through valve 
6 would have resulted in a ruptured relief disc. 

Valve was closed when evacuating any part of the gas 
system. Valve was open at all other times. 

8 Valve to vacuum line. Valve was open when evacuating 

any part of the gas system. Valve was closed at all 
o the r time s . 


9 Valve to admit atmospheric pressure to the vacuum 

gage ionization tube. Valve 9 was full open when 
venting gas through valve 6. Valve was closed when 
evacuating any part of the gas system. Valve was 


open at all other times. 









. 














19 


Valve 

10 


11 


12 


13 


14 

15 


TABLE 1. - Compressibility apparatus valves (Con.) 

No. Function 

Valve between oil displacement pump and piston gage. 
Valve was open when measuring a pressure with the 
piston gage. Valve was closed to isolate the piston 
gage from the remainder of the oil pressure system. 

Valve to oil reservoir. Valve was open when filling 
the displacement pump with oil. Valve was closed at 
all other times. 

Valve between oil displacement pump, and oil mano¬ 
meter and differential pressure cell. Valve was 
open when measuring a pressure with the piston gage. 
Valve was closed to isolate the differential pres¬ 
sure cell and oil manometer from the remainder of the 
oil pressure system. 

Valve to the oil manometer. Valve was open when the 
differential pressure cell meter was zeroed. Valve 
was closed at all other times. 

Spare outlet valve from oil displacement pump. Valve 
was closed during all compressibility runs. 

Valve to oil reservoir. Valve was open during all 


compressibility runs. 





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Valve 

16 


TABLE 1. - Compressibility apparatus valves (Con.) 

No. Function 

Valve from oil displacement pump to compressibility 
bomb jackets and Heise Bourdon tube gage. The oil 
jackets were not used during a compressibility run; 
therefore, valve was open during all compressibility 


runs. 















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21 


EXPERIMENTAL PROCEDURE 

The Burnett compressibility method has been described in the 
literature (9 ). The following description outlines the procedure 
used to obtain the data recorded in this report. 

The temperature of the bomb bath was lowered to 0° C by pumping 
refrigerated fluid through the compressibility bath heat exchange 
coils. The compressibility bath temperature controller and the re¬ 
frigerator mercury thermoregulator were adjusted until the compres¬ 
sibility bath temperature was maintained at the desired level. The 
temperature of the external tank was controlled at about -3.5° C in 
order to compensate for heat leak and maintain the compressibility 
bath at 0° C. 

The gas side of the differential pressure cell was opened to 
atmospheric pressure. The valve to the oil manometer was opened, 
and the level of the oil in the manometer was adjusted to corres¬ 
pond to the level of the diaphragm of the differential pressure 
cell. The readout meter of the differential pressure cell was set 
at maximum sensitivity, and the meter was zeroed. 

The gas system of the compressibility apparatus was evacuated, 
then purged and filled to supply cylinder pressure with test gas. 

The evacuated volume of the compressibility apparatus was filled 
with test gas by slowly expanding the gas from into while 
simultaneously maintaining a slight overpressure on the oil side of 
the differential pressure cell diaphragm. The valve between and 
was closed, and was filled with test gas to a high pressure 



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22 


by use of the Corblin gas compressor. Then was filled with test 
gas at high pressure by expansion from while simultaneously 
maintaining a small overpressure on the oil side of the differential 
pressure cell diaphragm by use of the oil displacement pump. The 
valve was closed between and , and the gas in was vented to 
the atmosphere. Volume was evacuated with the vacuum pump. The 
rather awkward filling procedure described above was necessary be¬ 
cause the compressor and compressor controls were located in one 
room, the remainder of the compressibility apparatus was located in 
another room, and it was necessary to avoid large overpressures on 
either the oil or gas sides of the differential pressure cell dia¬ 
phragm. 

The gas in was allowed to reach temperature equilibrium. 

Gas pressure in was balanced with oil pressure by adjusting 

weights on the piston gage until the differential pressure cell meter 
indicated the null position. Temperature equilibrium was assumed to 
be established when the piston gage indicated a stable pressure. The 
designations of weights on the piston gage, piston gage temperature, 
barometer scale reading, barometer temperature, relative humidity, 
and the resistance of the platinum resistance thermometer were re¬ 
corded. The differential pressure cell was closed off from the oil 
pump and piston gage, and the piston gage was lowered to its rest 
position by slowly decreasing the pressure with the oil displacement 
pump. The piston gage was isolated from the system by closing the 
valve between the oil pump and the piston gage. Oil pressure was 
raised to equal the gas pressure by use of the oil displacement pump, 

















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23 


and the valve to the differential pressure cell was opened. The 
vacuum in was measured with the vacuum gage, the valve to the 
vacuum pump was closed, and the high-pressure exhaust valve from 
was closed. Gas in was slowly expanded into the evacuated V ^ • 

A small overpressure was maintained on the oil side of the differen¬ 
tial pressure cell diaphragm during the expansion. It was important 
that any overpressure be maintained consistently on the oil side of 
the diaphragm. If large overpressures had been applied alternately 
to the oil and gas sides of the diaphragm, there would have been a 
change in the zero position of the diaphragm. Zero shift of the 
diaphragm due to large overpressures, alternately on the oil and gas 
sides of the diaphragm, could have introduced errors of as much as 
0.02 psi in the measured pressures. 

Gas in and was allowed to reach thermal equilibrium. 

The piston gage was isolated from the system, and the differential 
pressure indicator was maintained in the zero position with the oil 
displacement pump as the expansion valve between and was 
slowly closed. After the expansion valve was closed, gas in V 9 was 
vented to the atmosphere, and was evacuated. The valve to the 
piston gage was reopened. Weights on the piston gage were read¬ 
justed until a null position was indicated by the differential pres¬ 
sure cell meter. All of the necessary observations were recorded. 
Then another expansion was made from into an evacuated V . The 
measuring and expansion sequence was continued until the lowest 
pressure that could be measured with the piston gage was reached. 


' 

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24 


CALCULATION OF CORRECTED PRESSURES FROM 
THE EXPERIMENTAL OBSERVATIONS 

A computer program was written, by the Data Processing Branch, 
to calculate corrected absolute pressures from the experimental ob¬ 
servations. Explicit instructions were given to the Data Processing 
group for each step in the pressure calculations. 

The first step of the calculations was to evaluate a corrected 
barometric pressure from the observed barometer scale reading and 
barometer temperature. National Bureau of Standards Monograph 8 (8) 
was used as a reference for reduction of barometer readings to 
standard conditions. 


Le t: R 


uncorrected barometer scale reading, mm 
barometer temperature, °C 


R = barometer reading corrected for temperature effects, 


R 


mm 


R = barometer reading corrected for gravity effects, mm 
R = barometer reading corrected to standard conditions, 


mm 


R + C 
s t 


C = barometer temperature correction, mm 


(s-m)t b R s 

"t = mt — t 1 )’ reference (8), page 28 

b 

s = coefficient of linear expansion of barometer scale 

__ r 

(brass) = 18.4 x 10 per °C, reference (8) , page 28 
m = mean cubical coefficient of thermal expansion of 


mercury 



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. 





25 


m x 



R 

g 

C 

g 


c 

g 



R 

c 

760 


18144.01 + 0.7016t, + 0.0028625t^ + 0.000002617^ 

b b b 

per °C (2), reference (8), page 4 

R + C 
t g 

barometer gravity correction 


§1 ~ § s 

- R (3), reference (8) , page 33 

S s 

-2 

local acceleration of gravity = 979.4091 cm sec 

(li) 

standard acceleration of gravity = 980.665 cm sec 

R + C + C + C , mm 
s t g c 

calibration correction provided by the National 
Bureau of Standards for Henry J. Green barometer 
Serial No. 13346, (_3) = +0.06 mm 

corrected barometer reading, standard atmospheres 


The next step was to calculate a corrected piston gage pressure 
from the experimental observations. National Bureau of Standards 
Monograph 65 (10) was used as a reference for reduction of piston 
gage data. Equation (4) was used to calculate a gage pressure 


M a (1 " P a /p b )g l /g s 

P g “ A (1 + bP )[1 + c(t - 25)] + C d 


( 4 ) 


g 


g 


for piston gage, Serial No. 9274. The calibration constants for 
piston gage, Serial No. 9274 were provided by Ruska Instrument 
Corporation. 


P = corrected gage pressure, psig 

























’ . 













































































26 


M - sum of the individual masses of the weights on the 

3 

piston gage, lbs 

-3 

p = density of air, gms cm 

3 

5/ -3 

P b = density of brass— =8.4 gms cm 


5/ The large piston gage weights were machined from 303 stainless 
steel. The very small weights were probably constructed of 
aluminum. All of the weights were calibrated by Ruska Instru¬ 
ment Corporation by comparison in air against class S standard 
weights. The standard weights used by Ruska Instrument Corpora¬ 
tion were calibrated by the National Bureau of Standards and 

_ 3 

were traceable to brass standards with a density of 8.4 gms cm 
The calibrated piston gage weights were reported by Ruska Instru¬ 
ment Corporation as apparent mass in air against brass standards; 

-3 

therefore, the density of brass of 8.4 gms cm was used in 
equation (4) rather than the actual density of the weights; 
reference (10) , page 3. 



o 


b 


c 

t 

g 


= local acceleration of gravity = 979.4091 cm sec 

-2 

= standard acceleration of gravity = 980.665 cm sec 

= piston gage area at 25° C and zero pressure = 0.0260416 

. 2 
m 

= piston gage pressure distortion coefficient = - 3.5 x 

m " 8 -- 1 

10 ps l 

= piston gage temperature coefficient = 1.7 x 10 °C L 
= piston gage temperature, °C 




























. 

















. 








































































27 


C, - differential pressure cell correction = 1.85 x 10 P 
d g 

Barieau (_1) presented equations for the calculation of the den¬ 
sity of moist air. 

Pa ' Pof 76^ (1 - °- 37807 ^ T ^ 

_6/ Equation (5) gave the density of moist air in gms liter ^ when 

used with a of 1.2932 gms liter ^. The density was changed 

-3 

to gm cm for use in equation (4). 


-f- = 1 - 0.000602 ^y~ - l) + (0.00254y + 0.0758y 2 ) 

? R 

-(0.0000105 + 0.0000131y + 0.00131y ) t fc y^ (6) 

T = absolute temperature = (273.15 + t,)°K 

b 

= absolute temperature of the ice point = 273.15° K 

y = mole fraction of water vapor 

p = 1.2932 gms liter ^ 

o 

Equation (7) was assumed to be valid for 

P x 760 x H 

y - — r- (7) 

C 

the calculations of this report. 

P = vapor pressure of liquid water, standard atmospheres 
s 

H = relative humidity expressed as a decimal fraction 


























, 
















































































28 


Osborne, Stimson, and Ginnings (13) presented equation (8) for 
calculation of the vapor pressure of water. 


1Og 10 P s 


= -3.142305 


3 3 

10 _ 10 

"F “ 373. 


is)*’-* 


-0.0024804(373.16 - T 7 ) 


( 8 ) 


t' = (273.16 + t ) °K 


The density of air was calculated using equations (5), (6), 

(7), (8), the corrected barometric pressure, the room temperature 
(t^) , and the observed relative humidity for each experimental piston 
gage pressure. 

An approximate piston gage pressure was obtained by substitution 
of the sum of the masses of the weights on the piston gage, the cal¬ 
culated density of air, the piston gage temperature, and the calibra¬ 
tion constants into equation (9) . 


P 


g(approx.) 


V 1 ~ ^ h b> Sj /8 s 

A [1 + c(t - 25)] 
o g 


(9) 


The approximate gage pressure calculated from equation (9), the 
experimental data, and the calibration constants were substituted 
into equation (4); and a new gage pressure was calculated. The new 
gage pressure was substituted back into equation (4) along with the 
experimental data and calibration constants; and another gage pres¬ 
sure was calculated. The iteration procedure was continued until 
the change in the calculated gage pressure was less than 0.0001 psig. 
The final pressure was accepted as the corrected piston gage pressure. 



























. 

* 

. . %V • 




















































































29 


Constants used by Ruska Instrument Corporation in the calibra¬ 
tion of piston gage, Serial No. 9274 were: 


1 in = 2.54 cm exactly 

1 lb = 453.5924 gms 


An atmosphere in terms of the constants supplied by Ruska 
Instrument Corporation was: 


1.013250 x 10 6 x (2.54) 2 

453.5924 x 980.665 


14.69594780 psi 


Ruska piston gage pressure in psig was divided by 14.69594780 to 
obtain gage pressure in atmospheres. Absolute pressure in atmos¬ 
pheres was obtained by adding the barometric pressure in atmospheres 
to the piston gage pressure in atmospheres. 

COMPOSITION OF THE TEST GAS 

An experiment was run to determine if any impurities were in¬ 
troduced into the test gas while filling the compressibility bombs 
to the initial high pressure. An analyzed cylinder of grade A 
helium was attached to the inlet of the gas compressor. The gas sys¬ 
tem was evacuated and purged with test gas, and the bombs were filled 
to an initial pressure of about 10,000 psi. The filling of the bombs 
was carried out exactly as it would be done for a compressibility run. 
Gas was vented from the bombs, and a sample of the gas was trapped 
for analysis. The compressibility bombs were filled three times to 
pressures of about 10,000 psi, and three samples were trapped for 
analysis. A sample taken directly from the supply cylinder and the 
three vent samples were analyzed by high-pressure mass spectrometry. 














• . 









































30 


The analyses are recorded in table 2. Examination of the data of 
table 2 indicates a slight increase in the nitrogen and oxygen con¬ 
tent of the vent samples over that of the cylinder sample; however, 
the increase in total sample impurities is considered negligible 
and probably occurred during the sampling procedure rather than 
during the bomb filling procedure. 

A total of twenty-two compressibility runs were made with helium 
at 0° C. Three helium cylinders were used to supply sample gas for 
the twenty-two runs. Analyses of impurities of each cylinder are 
recorded in table 3. The particular cylinder used for each compres¬ 
sibility run is listed below. 


Run No. 

Cylinder No. 

Run No. 

Cylinder No. 

HE-0-1 

H-135022 

HE-0-12 

AEC107250 

HE-0-2 

H-135022 

HE-0-13 

AEC107250 

HE-Q-3 

H-135022 

HE-0-14 

AEC107250 

HE-0-4 

H-135022 

HE-0-15 

AEC107250 

HE-0-5 

H-135022 

HE-0-16 

AEC107250 

HE-0- 6 

H-135022 

HE-0-17 

AEC107250 

HE-0- 7 

H-135022 

HE-0-18 

AEC107250 

HE-0-8 

H-135022 

HE-0-19 

AEC107250 

HE-0-9 

AEC107250 

HE-0-20 

AEC103941 

HE-0-10 

AEC107250 

HE-0-21 

AEC103941 

HE-0-11 

AEC107250 

HE-0-22 

AEC103941 



■ 


. 




f 








' 





















31 


TABLE 2. - Analysis 

of vent 

samples 

, parts 

per million 

by volume 




impurities in 

he 1ium 





H 2 

CH, 

4 

Ne 

N 2 

°2 

Ar 

CO 

Sample direct from 








Cylinder No. 25598 

0.9 

0.2 

20.0 

3.5 

0.7 

0.1 

0. 

Vent sample No. 1 

1.2 

0.3 

17.8 

18.5 

6.9 

0.2 

0. 

Vent sample No. 2 

1.3 

0.4 

16.8 

9.7 

1.8 

0.1 

0. 

Vent sample No. 3 

0.9 

0.5 

19.4 

12.3 

2.1 

0.1 

0.- 


TABLE 3. - 

He1ium 

cylinder ana 

lysis, 

part 

per million 

by volume 




impurities 

in helium 




Cylinder 

Number 

H 2 

CH, 

4 

H 2° 

Ne 

N 2 

°2 

Ar 

C°2 

Tota 1 

H-135022 

0.4 

0.0 

0.7 

15.2 

1.4 

0.3 

0.0 

0.0 

18.0 

AEC107250 

0.0 

0.0 

0.8 

11.8 

2.5 

0.6 

TrV 

Tr. 

15.7 

AEC103941 

0.3 

0.0 

0.9 

11.7 

0.6 

0.1 

0.0 

0.1 

13.7 


JL/ Tr. indicates less than 0.05 parts per million. 









• - . ' • 







/ 

• 


J 









. 



■■■ •. ■ ■ 







. : 
















• 


























































32 


COMPRESSIBILITY-BOMB BATH TEMPERATURES 


Temperature measurement with Leeds & Northrup platinum resistance 
thermometer Serial No. 1586182 has been discussed in Helium Research 
Center Internal Report No. 53 (.2). Platinum resistance thermometer 
Serial No. 1586182 was mounted in the compressibility-bomb bath, and 
was used to measure the temperature of the bath fluid. Thermometer 
resistance measurements were made with the G-2 Mueller bridge commu¬ 
tator in both the N and R positions. Thermometer resistance measure¬ 
ments were made each time a piston gage pressure measurement was made. 
The average bath temperature for a complete compressibility run was 
assumed to be representative of the actual sample temperature. The 
large mass of the compressibility bombs tended to smooth out minor 
rapid fluctuations of the bath temperature. The average measured 
bomb bath temperature and the standard deviation of the average mea¬ 
sured bomb bath temperature are recorded in table 4, f or each of the 
twenty-two compressibility runs. Temperatures calculated from the 
measured resistances of platinum resistance thermometer Serial No. 
1586182 are in terms of the International Practical Temperature Scale 
(IPTS). 

CALCULATION OF CONSTANTS AND COMPRESSIBILITY FACTORS 
FROM THE OBSERVED PRESSURES 

Initially, the assumption was made that compressibility factors 
for helium could be represented by equation (10) over the experimental 
pressure range. 


Z 


r 


1 + BP + CP 2 


r r 



( 10 ) 


■ * 

. 








33 


TABLE 4. - Compressibility-bomb bath temperatures 


Run No. 

t ,°C(IPTS) 

Run No. 

t ,°C(IPTS) 

HE-0-1 

-0.006+0.001 

HE-0-12 

+0.003+0.000 

HE-0-2 

+0.002+0.001 

HE-0-13 

+0.002+0.001 

HE-0-3 

-0.001+0.001 

HE-0-14 

+0.003+0.001 

HE-0-4 

-0.001+0.000 

HE-0-15 

+0.002+0.000 

HE-0-5 

+0.001+0.001 

HE-0-16 

+0.003+0.001 

HE-0-6 

+0.003+0.001 

HE-0-17 

-0.001+0.001 

HE-0-7 

+0.002+0.001 

HE-0-18 

+0.002+0.001 

HE-0-8 

+0.004+0.001 

HE-0-19 

-0.001+0.001 

HE-0-9 

+0.003+0.001 

HE-0-20 

0.000+0.001 

HE-0-10 

+0.002+0.001 

HE-0-21 

+0.002+0.001 

HE-0-11 

+0.001+0.001 

HE-0-22 

0.000+0.001 













♦ 




• . 








































. / 




































34 


f 

r 


(1 + a l+2 P P (1 + Qf l+2 F 2 ) ’ • ' (1 + Q? H-2 F r' ) 

(1 + a P 0 )(l + OjPp ... (1 + 


(ll )- 7 


2/ The coefficient a 2 corresponds to the coefficient a of refer¬ 
ence ( 12) , equation (4), page 6. The coefficient a corresponds 
to the coefficient 3 of reference (12), equation (4), page 6. 



N 


a 


1+2 


01 


1 


compressibility factor at P^ 

constant evaluated from the experimental pressures 

constant evaluated from the experimental pressures 

t Vi • 

pressure before the r expansion 
pressure after the rth expansion 
expansion number =0, 1, 2, 3, ... 
pressure before the first expansion 
compressibility factor at Pq 

factor to correct for elastic distortion of the 

compressibility bombs 

V° + V° 

1 2 

—- = isothermal volume ratio at zero pressure 


isothermal internal-pressure distortion coefficient for 

"6 - 1 

volume V 1 +V 2 = 1.6678 x 10 atm at 0° C, reference (2), 
page 34. 

isothermal internal-pressure distortion coefficient for 
volume V = 1.6671 x 10" atm at 0° C, reference (2), 


page 34. 








V 








' 

, 
























































35 


Least squares calculation of the constants B, C, and N; 
evaluation of the standard errors of the constants; calculation 
of compressibility factors; and evaluation of the standard errors 
of the compressibility factors from the experimentally observed 
pressures were discussed in Helium Research Center Internal Report 
No. 69 (Rev.) (12). A computer program was written by the Data 
Processing group in compliance with instructions from the authors 
of Internal Report No. 69 (Rev.), to carry out the extensive calcu¬ 
lations required in the data evaluation. 

The computer-calculated results were printed out directly on 
multilith masters. The experimental pressures, least squares calcu¬ 
lated pressures, constants, standard errors, variances, and covari¬ 
ances were printed out. The computer printed out the numerical 
quantities in "E format." For example, 6.4728895 E&02 represented 

6.4728895 x 10 2 , 7.8217009E-00 represented 7.8217009, and -3.77627E-04 

-4 , 

represented -3.77627 x 10 . A weighting factor of one was used for 

all of the calculations of this report. No correction was applied 

to any of the runs for the difference between the actual average 

bath temperature and 0° C. 

The column of numbers under the heading R in table 5 denotes 
the expansion number. The observed experimental pressures for each 
run are given in table 5. The least squares calculated pressures; 
the difference between the observed experimental pressures and the 
calculated pressures; and the relative difference of the observed 
pressures and the calculated pressures are recorded in table 5. The 
least squares calculated constants N, B, and C of equation (10) are 








' 








■ 














* 





















' 
















36 


recorded in table 5. The standard errors of N, B, and C are desig¬ 
nated as SN, SB, and SC, respectively; and are listed in table 5. 

The variances of N, B, and C are denoted as S2N, S2B, and S2C, 
respectively; and are recorded in table 5. The covariances of BC, 

BN, and CN are denoted as S2BC, S2BN, and S2CN, respectively; and 
are listed in table 5. 

The variances of pressures calculated at even increments of 
pressure, the covariances of BP for even increments of pressure, 
and the covariances of CP at even pressure increments are recorded 
in table 6 under the headings S2P, S2BP, and S2CP, respectively. 

Compressibility factors and standard errors of the compressi¬ 
bility factors calculated at even increments of pressure are listed 
in table 7 under the headings Z and SZ, respectively. 

The detailed methods used to calculate the various constants, 
variances, covariances, and standard errors were discussed in refer¬ 
ence (12). Data are recorded in tables 6 and 7 to pressures of 1,000 
atmospheres. The data are recorded to 1,000 atmospheres with a full 
awareness of the attendant hazards involved when extrapolating data 
with an empirical equation beyond the range of the experimental data. 

Tables 5, 6, and 7 do not conform to the Bureau of Mines Style 
Guide due to limitations of the computer printout; however, consider¬ 
able time and money were saved by eliminating the extensive typing 
and proofreading that would have been required for the tables. 

Values for the compressibility apparatus zero pressure volume 
ratio (N) for each of the twenty-two runs are recorded in table 8 
along with the value of the average N, the standard error in the 













. 



















<\i m -4" m so r- 


37 


TABLE 5.- EXPERIMENTAL PRESSURES? CALCULATED PRESSURES, 

CONSTANTSg STANDARD ERRORS? VARIANCES, 

AND COVARIANCES 


RUN NO. HE~0“1 


R PoOBScATM* 


P ?CALo 9 ATMc 


P v OBS®-P s CAL o 


P,OBS®~P9CAL. 
P j OBS • 


0 

1 


6..4728895EC02 
2o 8125289EC02 
1«3168470E£02 
60 3853510ECOI 
3.I49I659EC01 
1o 5661273E COl 
7 ®82170G9E-00 
3o915I145E-00 


6.4728895EC02 
2o 8125327EC02 
1o 3168271EC02 
6 ® 3856222EC01 
3 o1492607EC01 
I•5660585EC01 
7•8196 732 £=■ 00 
3o 9125240E-=00 


0o00000E-99 
•=3o79122E“04 
1® 98702E-03 
“2 « 71177E-03 
“9 0 47268E-04 
6 ® 87580E-G4 
2o02770E“03 
2 o 59048E“03 


0* 00000E-99 
-1o 34797E-06 
1.50892E-05 
-4.24687E-05 
-3.GG799E-05 
4.39032E-G5 
2•5924QE-04 
6.61662E-04 


SUM OF NEIGHTED SQUARES OF THE RESIDUALS 2.36379E-05 


CONSTANTS AND STANDARD ERRORS 


N 

1o994538449E= 

■GO 

SN 

1o03067E“04 

B 

5«27866I085E= 

-04 

SB 

7 * 50992E-07 

C 

-4*789121598 E-= 

-08 

SC 

5® 51862E-10 


VARIANCES AND COVARIANCES 


S2N 1 © 06228E—08 
S2B 5o63989E“13 
S2C 3o 04552E—19 
S2BC ~4 0 1G648E™16 
S2BN -7 o 45204E™11 
S2CN 5 ® 23146E-14 







































■ 





























































































.38 


TABLE 5.- EXPERIMENTAL PRESSURES* CALCULATED PRESSURES* 

CONSTANTS* STANDARD ERRORS, VARIANCES* 

AND COVARIANCES 


RUN NO, HE-O-2 


R P *OBS o * ATM. 


P ?CAL o * ATM. 


P 9 OBS o—P y CAL• 


Pj»QBS»-P»CAL« 

PiOBS * 


0 

1 

2 

3 

4 

5 

6 
T 


6*9039330EC02 
2o9760733EC02 
l* 3883415ECQ2 
6,7203083E CO 1 
3.3114887E&01 
Io 6462213EE0 L 
8* 2197040E-00 
4 0 113961IE“00 


6« 9039330ES02 
2 » 9760778EG02 
I-3883178EE02 
6.7206234E801 
3*31164G8EC0I 
1•6460883EC01 
8,2I73777E-Q0 
4,1109784E-0G 


Oo 00000E-99 
~4o 49502E-04 
2„36761E-03 
~3,15076E-03 
-1® 5204IE-03 
1o 33065E-03 
2 o 32625E—03 
2 o 98266E-03 


0* 000G0E-99 
-1.51038E-06 
1.70535E-05 
—4.68841E—05 
-4.59134E-05 
8.08308E-05 
2.83010E—04 
7.25011E-04 


SUM OF WEIGHTED SQUARES OF THE RESIDUALS 3.41250E-05 



CONSTANTS AND 

STANDARD 

ERRORS 

N 

1.994596600E*= 00 

SN 

1.17272E-04 

B 

5.270983385E-04 

SB 

8•08440E-07 

C 

“4.693297998E—08 

SC 

5« 54453E-10 


VARIANCES AND COVARIANCES 


S2N 1.37527E-08 
S28 6« 53576E—13 
S2C 3o 07418E~ 19 
S2BC -4* 44106E-16 
S2BN -9,I2909E”11 
S2CN 5 ® 98045E-14 














































































































' 
























































"J O' Ut ^ W M 


39 


TABLE 5. — EXP ERIMENTAL PRESSURES, CALCULATED PRESSURES, 

-INS TANTS. STANDARD ERRORS » V ARIANCES, 

AND COVARIANCES 


RUN NGo HE-0-3 


R P?OBSo, ATM. 


P,CALo T ATM. 


P,OBS«-P?CAL o 


P T OBSo -P,CAL e 

P ? OB S• 


0 

I 


7 o 0128236EC02 
3.0170799EC02 
1 o 4061376EG02 
6 . 8033559EC01 
3o 35I7320EC01 
1•66605 72EG01 
8o31860ILE“00 
4*1639855E-GO 


7« 0128236EC02 
3o 0170849EC02 
1o 4061i12E £02 
6.8037124E £01 
3.3518813EC01 
1.665933 2E CO1 
8•3161327E—00 
4o1603444E-0G 


0.Q0000E-99 
“4o99133E-04 
2«. 64039E-03 
-3.56490E-03 
“1.49289E-03 
1o 23916E-03 
2o 46844E-03 
3.64111E~03 


0.00000E-99 
-1.65435E-06 
1.87776E-05 
-5.2399IE-05 
-4.45411E-05 
7.43771E-05 
2.96737E-04 
8.74430E-04 


SUM OF WEIGHTED SQUARES OF THE RESIDUALS 4.30445E-Q5 



CONSTANTS AND 

STANDARD 

ERRORS 

N 

1*994559047E~00 

SN 

1.29990E-04 

B 

5.277062588E-04 

SB 

8.84365E—07 

C 

-=4.739061450E-08 

SC 

5.96411E-10 


VARIANCES 


AND COVARIANCES 


S2N 1o 68975E-08 
S2B 7o 82102E— 13 
S2C 3.55707E-19 
S2BC “5o22569E“16 
S2BN ~1o1G699E-10 
S2CN 7*13077E-14 




















































' 

















































































cm 4* in no p- 


40 


TABLE 5. ~ EXPERIMENTAL PRESSURES , CALCULATED PRESSURES, 

CONST ANTS $ STANOARD ERRORS, VARIANCES, 

AND COVARIANCES 


RUN NQo HE-0-4 


R P,DBS o,ATM* 


P vCAL o,ATMo 


P,OB So“P,CAL o 


P,DBS.-P,CAL* 
P,OB S * 


0 

I 


7* 057452GE8Q2 
3 * 0337137E802 
1*4133952E8Q2 
6* 8373652E801 
3* 3682135E801 
1-6741807E801 
8.3590666E-00 
4*18263 9GE—00 


7*057452OE802 
3o0337184E802 
1c 41337GGE 802 
6o 8377158E801 
3* 3683467E801 
1 * 6740349E801 
8 o 3563114E-00 
4c1803480E—00 


0 *00000E—99 
“4.69417E-04 
2c 51442E“Q3 
~3c 50620E-03 
“1« 33223E—03 
1 c 45779E-03 
2o75516E“03 
2* 29095E“03 


0* 00000E“99 
-I.547 33E~06 
1.77899E-05 
“5*12 800E-G5 
—3•955 30E-05 
8* 7 0753E-05 
3*29601E“04 
5.47730E-04 


SUM OF WEIGHTED SQUARES OF THE RESIDUALS 3*55755E~05 


CONSTANTS AND STANDARD ERRORS 


N 1.994588585E-00 
8 5*271687920E“04 
C -4.681194167E“08 


* SN 

1*17547E“04 

SB 

7•95328E“07 

SC 

5.32730E-10 


VARIANCES AND COVARIANCES 


S2N 1 * 38173E“08 
S2B 6*32546E“13 
S2C 2 * 83801E~19 
S2BC “4*19774E—16 
S2BN ~9c 00258E— 11 
S2CN 5o75964E“14 

































































f 


























. 














































































































































41 


TABLE 5.- EXP ER IMENTAL PRESSURESv CALCULATED PRESSURES, 

CONSTANTS, STANDARD ERRORS, VARIANCES? 

AND COVARIANCES " 


RUN NO. HE-O-5 


R P,G 8 S<» , ATM *> 


P 9 CAL 0 ,ATM. 


P,OBS.—P,CALo 


P,OBSo—P,CAL• 
P,OBSo 


0 

1 

2 

3 

4 

5 

6 
7 


6.9787955ECG2 
3 o G041472ECG2 
1«40G5441EC02 
6.7772168EC01 
3.339019IE&01 
1.6597 313EC01 
8.2868246E-00 
4.1479419E-00 


6o9787955EC02 
3o 0041521EE02 
1 o 4005180E &02 
60 7775718EC01 
3.3391591EC0I 
1.6596132EC0I 
So 2844129E-00 
4o1443432E-00 


0o00000E-99 
“4o 93091E-04 
2o 61096E-03 
“3.55052E-03 
-1.3994GE-03 
1«I8I10E-03 

2 ® 41166E-03 

3 * 59864E—03 


0 „ 0000GE-99 
-U64136E-06 
1.86425E-05 
—5.23890E-Q5 
-4.191G5E-05 
7.11626E-05 
2.91024E-04 
8.67573E-04 


SUM OF WEIGHTED SQUARES OF THE RESIDUALS 4.17861E-05 



CONSTANTS AND 

STANDARD 

ERRORS 

N 

1.994645905E-00 

SN 

1o286G9E~04 

B 

5.268807189E-04 

SB 

8.78420E-07 

C 

—4.666713741E—08 

SC 

5.95524E”!0 


VARIANCES AND COVARIANCES 


S2N 1o 65404E—08 
S28 7o 71623E- 13 
S2C 3o 54649E-19 
S28C —5.18287E-16 
S28N —1o 08785E-10 
S2CN 7o04448E“14 





















































• 























. 




* 










r^V.-Jr . 



















































, 

























42 


TABLE 5.- EXPERIMENTAL PRESSURES, CALCULATED PRESSURES* 

CONSTANTS, STANDARD ERRORSt VARIANCES, 

AND COVARIANCES 


RUN NO* HE—0-6 


R PtOBS.* ATM* 


P,CAL., ATM. 


P,OBS.-P»CAL. 


P,OBS.-P,CAL. 

P,OBS. 


0 

1 

2 

3 

4 

5 

6 
7 


7.0298868EC02 
3.0233845EC02 
1*40888358£02 
6* 8163698ECO1 
3.3579834EC01 
1•669Q781EC01 
8•3334615E-00 
4*1709998E—00 


7•0298868EE02 
3.0233882EC02 
1.4088639E CO2 
6*816616GE£01 
3*3581280E£01 
1•6690040E £01 
8 •3313413E-00 
4*1679046E-00 


0« OOOOOE—99 
-3.76107E-04 
1 * 95427E-03 
-2•46256E-03 
-1.44524E-03 
7 * 40724E—04 
2.I2015E-03 
3•09523E-03 


O.OQOOOE-99 
— 1* 24399E-06 
1 * 38710E-05 
-3.61272E-05 
-4.30390E-03 
4.43792E—05 
2* 54414E—04 
7.42083E-04 


SUM OF WEIGHTED SQUARES OF THE RESIDUALS 2.67377E-05 


CONSTANTS AND STANDARD ERRORS 


N 1.99457 6605E—00 
B 5.274084928E-04 
C -4.703667006E-08 


SN 1•02241E-04 
SB 6* 94109E-07 
SC 4* 66884E—10 


VARIANCES AND COVARIANCES 


S2N 1*045328-08 
S28 4.81787E—13 
S2C 2.17981E—19 
S2BC -3.21Q71E—16 
S2BN —6.83373E—11 
S2CN 4.39047E—14 



















■ . 





* 4 . '■ 3 €. £ 
































































































































43 


TABLE 5. - EXPERIMENTAL PRESSURES, CALCULATED PRESSURESt 

CONSTANTS, STANDARD ERRORS, VARIANCES, 

AND COVARIANCES 


RUN NO. HE-0-7 


R PfOBS.fATM. 


P,QBS.-PyCAL. 

P 9 CAL.»ATM. P,OBS.-P,CAL. P,OBS. 


0 

1 

2 

3 

4 

5 

6 
7 


7.0208680ES02 
3.02008I2EC02 
1.4074887E 802 
6•8097837ES01 
3♦3548005E GO1 
1.6674984E COI 
8.3248260E-00 
4.I658969E-00 


7.0208680£802 
3.0200852E802 
1.4074672E802 
6.81QG872E801 
3.3549042EG01 
I•6673677E801 
8•3229256E-00 
4.163551OE—00 


0.00000E-99 
—4.00933E-04 
2.15122E-03 
—3.03519E—03 
-1.03785E-03 
1.30695E-03 
I.90Q33E-03 
2.34587E-03 


0.00000E-99 
-1.32756E-06 
I.52841E-05 
-4.45710E-05 
-3.09365E—05 
7•83782E—05 
2.28273E-04 
5.63113E-04 


SUM OF WEIGHTED SQUARES OF THE RESIDUALS 2.59005E-05 


CONSTANTS AND STANDARD ERRORS 


N 

I.994655145E-00 

SN 

1.00737E-04 

B 

5.267277664E-04 

SB 

6.84502E-07 

C 

—4.66466I038E—08 

SC 

4.61088E-10 


VARIANCES AND COVARIANCES 


S2N 1.G1480E—08 
S2B 4.68544E-I3 
S2C 2.I2602E-19 
S2BC -3.12698E-16 
S2BN -6.63999E-11 
S2CN 4.27218E-14 






























• - 
























































WA i Ui i>t A V 

















































































44 


TABLE 5.- EXPERIMENTAL PRESSURES, CALCULATED PRESSURES » 

CONSTANTS, STANDARD ERRORS, VARIANCES, 

AND COVARIANCES 


RUN NO. HE-0-8 


R PfOBS*,ATM. 


P,CAL.iATM. 


PyOBS.-PyCAL. 


PyOBS.-PfCAL. 
PyOBS. 


0 

1 

2 

3 

4 

5 

6 
7 


7.0061130ES02 
3.0144846E602 
1•4050824E602 
6.7985497EC01 


7.0061130ES02 
3.0144894E£02 
1•4050564ES02 
6.7989157E&01 


0.00000E-99 
-4.85326E-04 
2.60068E-03 
-3.65961E-03 
-1.24887E-03 
1.46235E—03 
2.48615E-03 
2.76066E-03 


0.00000E-99 
—1•60998E-06 
1.85091E-05 
-5.38293E-05 
-3.72863E-05 
8.78357E-05 
2.99091E-04 
6.63649E-04 


3.3494053E601 
1•6648795EC01 
8.3123743E-00 
4.1598289E-G0 


3.3495302E801 
1.6647332EG01 
8.3098882E-00 
4.1570683E-00 


SOM OF WEIGHTED SQUARES OF THE 


RESIDUALS 


3.78923E-05 


CONSTANTS AND STANDARD ERRORS 


N 

1.994644503E-00 

SN 

1.2206IE-04 

B 

5.265546450E-04 

SB 

8.30873E-07 

C 

-4.642499200E-08 

SC 

5.60943E-10 


VARIANCES AND COVARIANCES 


S2N 

1.48989E-08 

S2B 

6.90350E-13 

S2C 

3.14657E-19 

S2BC 

-4.61764E-16 

S2BN 

-9.76587E-11 

S2CN 

6.29753E-14 





















































; 






























' 




























































■ 






• . • 


























































45 


TABLE 5.- EXPERIMENTAL PRESSURES, CALCULATED PRESSURES, 

CONSTANTS, STANDARD ERRORS , VARIANCES, 

~ AND COVARIANCES 


RUN NG« H E - 0 - 9 


R P,OBS.,ATM• 


P s CAL *,ATMo 


P,GBS.“P»CAL. 


P,OBS.-P*CAL. 
" P,OBS* 


0 6.8457479EC02 

1 2•9540775EC02 

2 I.3787047EC02 

3 6.6752988EC01 

4 3.2896560EC01 

5 1.6350585EE01 

6 8.1629533E-00 

7 4.0856389E—00 


6.8457479E&02 

2. 9540786EC02 
1.3786989EC02 
6.6753938EC01 

3. 289602IEC01 
I•6351594ES01 
8.1627075E-00 

4. 0835117E-QG 


0 » 000Q0E—99 
-1« G7909E—04 
5o80596E-04 
“9*49597E—04 
5* 38243E-04 
-Lo00854E-03 
2 o 45 852E-04 
2.1272IE—03 


O.OOOOOE-99 
-3.65290E-07 
4.21117E-06 
-1.422558-05 
I•63616E—05 
-6.16826E-05 
3.01180E-05 
5.20655E-04 


SUM OF WEIGHTED SQUARES OF THE RESIDUALS 7.14282E-06 


CONSTANTS AND STANDARD ERRORS 


H 1•994683005E~00 
8 5 * 269346921£“04 
C —4.6921IG033E-08 


SN 5.40394E-05 
SB 3.75194E-07 
SC 2.59678E-10 


VARIANCES AND COVARIANCES 


S2N 

2.92026E-09 

S2B 

1« 4077QE-13 

S2C 

6.74327E—20 

S2BC 

-9.65316E-17 

S2BN 

-1.95227E-11 

S2CN 

1.29067E”14 















































/ 









' 




























. 




































































• 





































■ 

















46 


TABLE 5.- EXPERIMENTAL PRESSURES h C ALCULATED PRFSSURES^ 

CONSTANTS > STANDARD ERRORS» VARIANCES*, 

ANO COVARIANCES 


RUN NO. HE“0“I0 


R P,GBS.,ATM 


P?CALo i ATM. 


P t OBS.-PtCAL. 


PfOBS.-PtCAL. 

P * OBS• 


0 

1 

2 

3 

4 

5 

6 
7 


7.0727559EC02 
3.0394992E802 
1.4L59267EC02 
6 * 8490921EG0I 
3.3738977EC01 
I•6767501EC01 
8.37 12273E-00 
4.I883028E-00 


7.0727559EC02 
3.0395032EC02 
1.4159044EC02 
6.8494449EE01 
3.3738994EC01 
1.6766889EC01 
8.3690432E-00 
4.1864612E-00 


0.00000E-99 
-4.03419E-04 
2.23308E—03 
-3.52876E-03 
-1.64789E-05 
6.12244E-04 
2•I8409E-Q3 
1. 84157E-03 


G.00000E-99 
-1.32725E-06 
1.57711E-05 
-5.152L6E-05 
-4.88423E-07 
3.65137E-05 
2.60905E-04 
4.39694E-04 


SUM OF WEIGHTED SQUARES OF THE RESIDUALS 2.6I383E-Q5 


CONSTANTS AND STANDARD ERRORS 


N 

I•994710232E-00 

SN 

1.00580E—04 

B 

5.26377 6675E-G4 

SB 

6.7909IE-07 

C 

-4.634771206E-08 

SC 

4.53855E-I0 


VARIANCES AND COVARIANCES 


S2N 

1.01163E-08 

S2B 

4.6I165E-I3 

S2C 

2.05984E-19 

S2BC 

-3« 05356E-16 

S2BN 

“6.57731E-11 

S2CN 

4.19859E-14 


































■ 













' 






















3* ?i 










v ' v '*•“•. ■ i ... < >■ i, 








. 















































' 















80-ioOS TTAC 6 . i - 
























































h ' i: • i 























. 


























47 


TABLE 5.- EXPERIMENTAL PRESSURES> CALCULATED PRESSURES, 

CONSTANTS, STANDARD ERRORS, VAR IANCES t 

AND COVARIANCES 


RUN NO. HE-O-11 


R PtOBS.»ATM. 


P,CAL o,ATM. 


P,OBS.-P*CAL. 


P,OBS«~P,CAL. 

P,OBS. 


0 

1 

2 

3 

4 

5 

6 
7 


7.034Q360EG02 
3.0249876EE02 
1.4096179EC02 
6.8196393EC01 
3.3595563EE01 
1•6697915EC01 
8.3369834E-00 
4.I713507E-00 


7 o 0340360E&02 
3o 0249920EC02 
I.4095944E&02 
6.8199749EC01 
3« 3596541EC01 
I,6696861E&01 
8.3343296E-00 
4.1691820E-00 


OoOOOOOE-99 
-4.37554E-04 
2.35324E-03 
-3.35541E-03 
-9.78234E-04 
L.05400E-03 
2 « 65375E-03 
2•16873E—03 


0.00000E-99 
—I.44646E~06 
I.66941E-05 
-4.92022E-05 
-2.91179E-05 
6.31218E-05 
3.18311E-04 
5.19912E-04 


SUM OF WEIGHTED SQUARES OF THE RESIDUALS 3.08017E-05 


CONSTANTS AND STANDARD ERRORS 


N 1 *994685709E“00 
B 5.265805061E“04 
C -4•652236204E“08 


SN I •09688E-04 
SB 7.44096E—07 
SC 5.00230E-10 


VARIANCES AND COVARIANCES 


S2N 

1 o 20315E-08 

S2B 

5* 53679E-13 

S2C 

2.50230E-19 

S2BC 

-3.68777E-I6 

S2BN 

-7.85947E-11 

S2CN 

5.04668E-14 






























' 






























' 

























• ■ 





















































































































































































48 


TABLE 5.- EXPERIMENTAL PRESSURES ? CAL CULATED PRESSURES, 

CONSTANTS? STANDARD ERRORS? VARIAN CES? 

AND COVARIANCES 


RUN NO. HE“Q"12 


R 


P?0BS.?ATM. 


P ?CAL.? AIM. 


P?OBS.-P*CAL. 


P,OBS.-P?CAL. 

-P ? OB'S". 


0 

1 

2 

3 

4 

5 

6 
7 


6.9905324EE02 
3.0086678E&02 
1.4025209EC02 
6.7865373EC01 
3.3435772EE01 
1.6618379EE01 
8.29691I1E-GG 
4.1518777E-00 


6 o 9905324EC02 
3.0086714E£02 
1.4025013E&02 
6 « 7868316EC01 
3.3436121E&01 
1.6617855EE01 
8.2950839E-00 
4.1496029E“00 


0 e0QG00E-99 
= 3*. 62422E—04 
1.96740E-03 
— 2 o 94273E-03 
-3.48478E—04 
5.24250E-04 
1o 8271IE-03 
2o27487E-03 


0.00Q00E-99 
-1.20459E-06 
1.40276E-05 
-4.336I3E-05 
-1.04223E-05 
3.15464E-05 
2.20216E-04 
5.479I3E-04 


SUM OF WEIGHTED SQUARES OF THE RESIDUALS 2.15713E-05 


CONSTANTS AND STANDARD ERRORS 


N 1.994680156E—00 
B 5.266261530E-04 
C —4.659S35926E—08 


SN 9.22708E-05 
SB 6.29262E-07 
SC 4.25857E-10 


VARIANCES AND COVARIANCES 


S2N 8o5139QE—09 
S2B 3.95971E“13 
S2C 1.81354E-19 
S2BC -2« 65499E-= 16 
S2BN —5.59103E-11 
S2CN 3o61412E“14 


































































. 






















































. - 

- 

N 

















































































































































49 


TABLE 5.- EXPERIMENTAL PRESSURES? CALCULATED PRESSURES, 

CONSTANTS, STANDARD ERRORS, VARIANCES, 

AND COVARIANCES 


RUN NOc HE~0“13 


R P,GBS*? ATM. 


P?CALo,ATM* 


P,OBS*-P,CAL. 


P,OB$.-P,CAL. 

P,OBS. 


0 

1 

2 

3 

4 

5 

6 
7 


7.1102445ES02 
3*0535233E£02 
1*4213544E C02 
6.8777416ESG1 
3*3877134ESOI 
1.6837357EE01 
8 « 4059 564E-G0 
4* 2075898E-00 


7o1102445ES02 
3*G535038E£02 
1 * 4214662E 802 
6 *8758200EC01 
3.3879038EC01 
I«. 6844952EC01 
8*4 131355E-00 
4*2113178E—00 


0 * 00000E-99 
1 * 94953E—03 
-l*11743E-02 
1 * 92156E-02 
-1 * 90374E—03 
-7.59531E-03 
“7«17913E-03 
“3* 72805E-03 


0.00000E-99 
6.38453E-06 
-7*86177E-05 
2.79388E-04 
-5*61956E-05 
—4•51099E—04 
-8.54053E-04 
-8.86031E-04 


SUM OF WEIGHTED SQUARES OF THE RESIDUALS 6.24658E-04 


CONSTANTS AND STANDARD ERRORS 


N l«993265919E-00 
B 5*382623171E—04 
C -5o442672.437E“08 


SN 4 * 88935E-04 
SB 3 * 29837E-06 
SC 2*18990E-09 


VARIANCES AND COVARIANCES 


S2N 2* 39057E—07 
S2B 1.08792E-11 
S2C 4* 79567E-18 
S2BC —7o15613E- 15 
S2BN — 1« 55300E—09 
S2CN 9* 84790E-13 



















































































. 





























































































-~jo-'U>4>ojro>—o 


50 


TABLE 5.- EXPERIMENTAL PRESSURES, CALCULATED PRESSURES, 

CONSTANTS * STANDA RD ERRORS, VARIANCES* 

AND COVARIANCES 


RUN NO* HE-O-14 


R P *OBS * » ATM* 


P * CAL * * ATM * P,OBS*-P,CAL. 


PyOBS.-PyCAL* 

P,OBS. 


6.9853895E&02 
3.0067567E802 
1 •401 6 95 3E 60 2 
6.7826865E&01 
3« 3416347EC01 
1 * 6609979EC01 
8.2927140E-00 
4.1500376E-00 


6*9853895EE02 
3* 0067608E £02 
1*4016736E£02 
6*T829815E £01 
3* 3417597EG01 
1 * 6608796EC01 
8« 2906178E-0Q 
4.1473923E-00 


0* 00000E-99 
“4* 09132E-04 
2 *17003E-Q3 
“2 * 94984E-03 
-1 * 25Q43E-03 
1«18318E-03 
2•09628E-03 
2 * 64529E-03 


0.00000E-99 
-1.36071E-06 
1.54814E-05 
—4* 34907E—05 
-3.74197E-05 
7.12335E-05 
2.52786E-04 
6* 37414E—04 


SUM OF WEIGHTED SQUARES OF THE RESIDUALS 2.79335E-G5 


CONSTANTS AND STANDARD ERRORS 


N 1 *9 946 70786 £-“00 
B 5*266671438E-04 
C -4.664502570E-08 


SN I * 05064E-04 
SB 7*16971E-07 
SC 4* 85596E-10 


VARIANCES AND COVARIANCES 


S2N 

1*10386E-Q8 

S2B 

5 *I4047E"13 

S2C 

2* 35804E-19 

S2BC 

-3*4494IE-16 

S2BN 

— 7 * 25362E-11 

S2CN 

4* 69253E-14 




















• • 




. 


















* 


































51 


TABLE 5.- EXPERIMEN TAL PRESSURE S ? CALCULATED PRESSURES, 

CONSTAN TS, STANDARD ER RORS? VARIANCES, 

AND COVARIANCES 


RUN NO. HE~0=15 


R 


P,OBS•,ATM . 


P,CAL *»ATM„ P t OBS o"P,CAL . 


P,OBS.—P,CAL. 

~p,obs:— 


7 * 0725396EC02 
3.G393974EC02 
1.4L58487EC02 
6.8487098EC01 
3.3735978EC01 
1 • 6766788EC01 

8 * 3707330E—00 
4.1888843E-00 


7.0725396EC02 
3.0394014E£02 
1 * 4158273ES02 
6.8490121ES01 
3* 3736872EC01 
1.6765924E £01 
8.3686287E-00 
4»1862931£—00 


0® OOOOOE-99 

— 3* 99883E-04 
2.14237E-03 

— 3 . 02290E-03 
-8.94679E-04 

8o 63908E-Q4 
2 * 10421E-03 
2o 5911IE-03 


O.OOOOOE-99 
-1.31566E-06 
1*513I4E-05 
-4* 41382E-05 
-2.65200E-05 
5.I5249E-05 
2.51377E-04 
6.18568E-04 


SUM OF WEIGHTED SQUARES OF THE RESIDUALS 2.65760E-05 


CONSTANTS AND STANDARD ERRORS 


N 

I.994688638£—00 

SN 

1.01424E—04 

B 

5.267589460E—04 

SB 

6.84869E-07 

C 

-4.663276458E-08 

SC 

4.57721E-I0 


VARIANCES AND COVARIANCES 


S2N 1.02868E—08 
S2B 4.69046E-13 
S2C 2<> 09508E- 19 
S2BC -3.10578E-16 
S2BN -6 ® 68896E-11 
S2CN 4o 26991E-14 
















































i 










• 














' 









• 
























































52 


TABLE 5.- EXPERIMENTAL P RESSURES; CALCULATED PRESSURES» 

CONSTANTS> STANDARD ERRORS, VARIANCES, 

AND COVARIANCES 


RUN NO. HE-0-L6 


R 


P ? OBS *»ATM. 


P i?CAL » 9 ATM. 


P,OBS.-P,CAL. 


P fOBS.—P»CAL. 

PtOBS. 


0 

1 

2 

3 

4 

5 

6 
7 


7.0575241E£02 
3.0337578EC02 
1.4L34198E£02 
6.8374213E801 
3.3681291EC01 
1•674Q047E801 
8.3570058E-00 
4.1813150E-00 


7.0575241EC02 
3.0337616E £02 
1.4133997EG02 
6.8377126££01 
3o3682113E£01 
1.6738841E£01 
8« 355Q967E-00 
4.1794973E-00 


OoOOOOOE-99 
— 3o 71762E-04 
2.01183E-03 
-2.91304E-03 
'-8.21297E-04 
1.2060GE-03 
1. 90902E-03 
1o 81770E-03 


0. OOOOOE-99 
-1.22542E-06 
1 .42338E-05 
-4.26043E-05 
-2.43843E-05 
7.20432E-05 
2.28433E-04 
4.34719E-04 


SUM OF WEIGHTED SQUARES OF THE RESIDUALS 2.17488E-05 



CONSTANTS AND 

STANDARD 

ERRORS 

N 

1.994710856E~00 

SN 

9.19145E-05 

B 

5.264497762E“04 

SB 

6.21732E-07 

C 

"4.63921 7186E—08 

SC 

4.16480E-10 


VARIANCES AND COVARIANCES 


S2N 8o 44827E—09 
S2B 3.86551E-13 
S2C 1o 73456E-19 
S2BC -2.56543E-16 
S2BN -5 o 50292E-11 
S2CN 3.52089E-14 





















































• 










- 


































































53 


TABLE 5.- EXPERIMENTAL PRESSURES, CALCULATED PRESSURES, 

CONSTANTS t STANDARD ERRORS t VAR IANCES > 

AND COVARIANCES 


RUN NO. HE-0-17 


R P t OBS * »ATM * 


P * CAL o ?ATMo 


P,OBS.-PtCAL. 


P,OBS.-P,CAL. 
PtCBS. 


0 

1 

2 

3 

4 

5 

6 
7 


6.9911233ECQ2 
3.0088594EC02 
1.4025861EE02 
6-7867489EC01 
3.3436121EG01 
1•6619056EC01 
8.2968869c-00 
4.1510115E-00 


6.9911233EC02 
3.0088631EE02 
1.4G25663E802 
6.7870445EC01 
3.3436701EC01 
1.6617918EC01 
8.2950036E-00 
4.1495070E-00 


0« 00000E-99 
~3«6195 IE-04 
1.97521E-03 
-2o95621E-03 
-5.80289E-04 
1.13 865E-03 
1.88329E-03 
1.50450E-03 


0.00000E—99 
-1.20295E-06 
1.40826E-05 
-4.35586E-05 
-1.73551E-05 
6.85147E-05 
2.26988E-04 
3.62443E-04 


SUM OF WEIGHTED SQUARES OF THE RESIDUALS 2.02152E-05 



CONSTANTS AND 

STANDARD 

ERRORS 

N 

1.994706908£—00 

SN 

8.93209E-05 

B 

5 o 266221013E—04 

SB 

6.09085E-07 

C 

-4.661046I45E—08 

SC 

4.12169E-10 


VARIANCES AND COVARIANCES 


S2N 7o 97823E—09 
S2B 3.70985E-13 
S2C 1.69883E—19 
S2BC -2.48726E-16 
S2BN —5o 23875E-11 
S2CN 3.38612E—14 


















































































































































■ 
























*-J O' U1 4>- OJ f\J 


54 


TABLE 5.- EKPE jUMENTAL PRESSURES« CALCULATED PRESSURES, 

CONSTANTS, STANDARD ERRORS, VARIANCES, 

AND COVARIANCES 


RUN NO. HE-0-18 


R 


P, OBS•*ATM® 


P f CAL o , ATMo P,GBS®-P»CAL«. 


P »OBSc-P »CAL* 

P * OBS* 


0 

1 


7«0498797E£02 
3*0309166E£02 
1*4121823E802 
6.8316532EEOI 
3.3653188E801 
1•6726X44E&01 
8 * 3501239E-00 
4»1762502E-G0 


7c0498797E802 
3*> 0309198E802 
1®4121650E£02 
6* 8319147ES01 
3.3653831EC01 
i.6724785E801 
8o3480459E-00 
4.1759443E-00 


0.00000E-99 
-3.14871E-04 
1«, 73309E-03 
“2.61551E-03 
-6.43610E-04 
1.35891E-03 
2 o 07799E-03 
3.05880E-04 


O.OOOOOE-99 
-1® 03886E-06 
1.22724E-05 
-3* 82852E-05 
-1.91248E-05 
8.12446E-05 
2*48858E-04 
7•32428E-05 


SUM OF WEIGHTED SQUARES OF THE RESIDUALS 1.66161E-05 


CONSTANTS AND STANDARD ERRORS 


N lo99472742GE“00 
B 5*263874634E—04 
C “4* 639439499E—08 


SN 8 * 04122E-05 
SB 5*444I3E“07 
SC 3.65 II7E—10 


VARIANCES AND COVARIANCES 


S2N 6*46612E-=09 
S2B 2o 96385E-13 
S2C I« 333I0E—19 
S2BC -1.96935E—16 
S2BN —4c 21555E—11 
S2CN 2c 70039E-14 























' 












- 




































r\j ro in 0 f- 


55 


TABLE 5.- EXPERIMENTAL PRESSURES, CALCULATED PRESSURES, 

CONST ANTS'", STANDARD £RR Q R$~j ~~YA R 1 ANCES , - 

AND COVARIANCES 


RUN NOo HE—0-19 


R P,DBS.,ATM* 


P,CAL o,ATMo 


P,GBS.-P,CAL. 


P,GBS.-P,CAL. 

P,GBS. 


0 

1 


6* 9586241EC02 
2.9965869EG02 
1.3972241E802 
6.7615486EC01 
3.331416QEE01 
1.6558741E801 
8.2667975E-00 
4*1368299E-00 


6o 9586241EC02 
2.9965909EC02 
1 * 3972019EC02 
6.7618841EC01 
3.3314617EC01 
1•6557686E801 
8o 2650413E-00 
4*1345410E-00 


O.OOGOGE-99 
-4.06652E-04 
2« 21898E—03 
-3.35508E—03 
-4o 57125E-04 
1.Q5532E-03 
1« 75617E—03 
2o 28883E-03 


0.00000E-99 
-1.35705E-06 
1.58814E-05 
-4.9620IE-05 
-1.37216E-05 
6.37322E-05 
2.12436E-04 
5.53282E—04 


SUM OF WEIGHTED SQUARES OF THE RESIDUALS 2.59914E-05 



CONSTANTS AND 

STANDARD 

ERRORS 

N 

1.994710157E-00 

SN 

U01684E-04 

B 

5.268100445E-04 

SB 

6.96171E-07 

C 

-4o675419052E—08 

SC 

4.73455E-10 


VARIANCES AND COVARIANCES 


S2N 1o 03396E-08 
S28 4o 84654E-13 
S2C 2 o 24160E-19 
S2BC -3.26562E—16 
S2BN -6o81649E”ll 
S2CN 4o 42799E—14 
















’ 



















































































































































56 


TABLE 5.- EXPERIMENTAL PRESSURES* CALCULATED PRESSURES, 

CONSTANTS, STANDARD ERRORS, VARIANCES, 

AND COVARIANCES 


RUN NO® HE-0-20 


R P,G 8 S ., ATM * 


P s CAL o 9 ATM*. 


P f Q 8 S.-P,CAL. 


P y Q 8 SP » CAL«. 

P*OBS. 


0 

1 

2 

3 

4 

5 

6 
7 


6 . 8620552ECQ2 
2 .9602082EC02 
1.38138 12EE02 
6.687 5363E SOI 
3.2955262ES01 
1•6381782ES01 
8.1792899E-00 
4.0925711E-00 


6.8620552ES02 
2.9602U7ES02 
1. 3813622ES02 
6 ® 6878096ESG1 
3* 2955934ES01 
lo6381001EC01 
80 1772633E-00 
4® 0907469E—00 


0oOOOOOE-99 
-3 o 52509E—04 
1o 89427E-03 
~2®73275E-03 
- 6 ® 72314E-04 
7o 817Q3E-04 
2 o 02653E-03 
1®82414E~03 


0* 00000E-99 
-I.19082E-06 
1.37128E-05 
-4.08634E-05 
-2.04008E-05 
4.77178E-05 
2.47764E-04 
4.45721E-04 


SUM OF WEIGHTED SQUARES OF THE RESIDUALS I.96779E-05 


CONSTANTS AND STANDARD ERRORS 


1.994698264E-00 

SN 

8.95215E—05 

5 o269146986£“04 

SB 

6.20268E-07 

-4c689610231E~08 

SC 

4.28203E-10 


VARIANCES AND COVARIANCES 


S2N 

80 0I410E—09 

S2B 

3® 84733E-13 

S2C 

1.83358E-19 

S2BC 

-2.63152E—16 

S2BN 

“5.34668E—11 

S2CN 

3c 52575E-14 








































































































’ 
























































































. 























* 




























57 


TABLE 5.- EXPERIMENTAL PRESSURES? CALCULATED PRESSURES, 

CONSTANTS y STANDARD ERRORS y VARIANCES, 

AND COVARIANCES 


RUN NO* HE-0-2I 


R P y DBS «iATM* 


P y CAL O ,ATMo 


PyOBS.-PyCALo 


Py08S»-PyCAL. 

P y OB S• 


0 

1 

2 

3 

4 

5 

6 
7 


7•7435393EGG2 
3* 2882507EC02. 
1 * 5234062EC02 
7 * 3499612E CO I 
3« 6158408EC01 
1 • 7959522EC01 
8.9632908E-00 
4.4841902E-00 


7®7435393E£02 
3«2882548E£02 
1® 5233842EC02 
7o 3 502566E £01 
3.6159824EC01 
1.7958392EC01 
8 » 9607633E-00 
4® 4816345E—00 


0 * 00G0GE-99 
-4«09534E-04 
2*19859E-03 
“2* Q5333E-Q3 
-l*41660E-03 
1 * 12 999E—03 
2« 52756E—03 
2« 55574E-03 


0.00000E-99 
-l*24544E-06 
1.44320E-05 
— 4* 018i5E-05 
—3.91778E-05 
6.29191E-05 
2.81990E—04 
5.69945E-04 ! 


SUM OF WEIGHTED SQUARES OF THE RESIDUALS 2.99278E-05 



CONSTANTS AND 

STANDARD 

ERRORS 

N 

1« 99477 5574E-00 

SN 

9.98009E-05 

B 

5*256600758E-04 

SB 

6 o 24062E-07 

C 

-4.540294049E-08 

SC 

3 ® 78373E-10 


VARIANCES AND COVARIANCES 


S2?N 9o 96023E—09 
S2B 3® 89454E“13 
S2C 1*43166E~19 
S2BC -2® 33919E-16 
S2BN -5® 99887E“11 
S2CN 3® 47328E”14 













































































' 


































































































58 


TABLE 5.- EXPERIMENTAL PRESSURES, CALCULATED PRESSURES, 

CONSTANTS, STANDARD ERRORS* VARIANCES, 

AND COVARIANCES 


RUN NO. HE-Q-22 


R P ,OBS.,A TM . 


P ? CAL o 9 ATM. 


PtOBSo-P ?CALo 


P,OBS.-P,CAL. 

P,OBS* 


0 

1 

2 

3 

4 

5 

6 
7 


5.8218590EE02 
2.5608357EC02 
1.2058177EC02 
5 • 8627782EEGI 
2.8951908EC01 
1.4406838EC01 
7.1967975E-00 
3.6018337E-00 


5c 8218590EC02 
2 o 5608380EC02 
1 * 2058057EC02 
5* 8629522EC01 
2.8952293EC01 
1•4406347EC01 
7.1955494E-00 
3.6007376E-00 


0o 00000E-99 
-=2.29970E-04 
1.20867E-03 
-Lq 73926E-03 
—3.85149E-G4 
4« 90996E-04 
lo24802E-03 
lo09616E"03 


O.OOOOOE-99 
-8.98029E-07 
1 • 0Q236E-05 
-2.96662E-05 
-1.33030E-05 
3.408Q8E-05 
1.73414E-04 
3.04333E-04 


SUN OF WEIGHTED SQUARES OF THE RESIDUALS 7.68737E-06 



CONSTANTS AND 

STANDARD 

ERRORS 

N 

1.994589770E~Q0 

SN 

6.43602E-05 

B 

5.282209668E-04 

SB 

5 o14062E-07 

C 

—4.863993404E“08 

SC 

4o23031E—l0 


VARIANCES AND COVARIANCES 


S2N 

4 0 14224E-G9 

S2B 

2.64260E-13 

S2C 

1o78955E“19 

S2BC 

-2 o15496E-16 

S2BN 

-3o18457E-11 

S2CN 

2«50415E-14 


































































> 






















































































































59 


TABLE 6.- VARIANCES AND COVARIANCES AT EVEN INCREMENTS OF PRESSURE 


RUN NOo HE-0-1 


PRESSURE, ATM o 

1* 000E-00 
2 * 000£-00 
5* 00QE-00 
1•000E SOI 
2•500E801 
.5.000ES01 
7.500EC01 
1.000E&02 
1.250EC02 
1.500EC02 
2•OOOE £02 
2.500EC02 
3 * 000EC02 
3.50QEC02 
4*000EC02 
4.500EC02 
5.000EC02 
6* 000ES02 

7 * 000E802 

8 * OOOE E02 
9« OOOES02 
1«000EC03 


S2P 

7o46782E-08 
1.98296E-07 
6.19199E-07 
1•22174E-06 
1 * 97179E—06 
1.92651E-06 
2® 32259E-06 
3.35699E-06 
4* 46108E-06 
5*11675E-06 
4® 665G6E—06 
4*18409E—06 
8o10615E-06 
1 •91595E = 05 
3 * 56562E—05 
5.10273E-05 
5® 6Q166E-05 
1® 71247E—05 
4* 98722E-05 
8*41450E-04 
4®15656E—03 
1® 34746E-02 


S2BP 

1o 89899E-1Q 
3®06081E—10 
5o 26663E-10 
7o 0825IE-10 
7 ® 44240E-10 
2® 7611 IE—10 
=3o02286E-10 

— 7o 9515 IE—10 
-1®13251E—09 

— 1® 29051E—09 
-1® 0735 7E-09 
-2 ® 50828E-10 

9*84031E-10 
2« 39695E-09 
3o 732 86E-09 
4o72525E-09 
5 ®10176E—09 
2® 9G787E-09 
“5o03746E-09 
-2 ® Q8755E-08 
—4® 66667E-08 
-8® 43664E-08 


S2CP 

-1.31276E-13 
-2*10827E-13 
-3* 59812E-13 
-4* 78Q46E-13 
—4* 79476E-13 
-I* 23385E-13 
2•96096E-13 
6* 43033E-13 
8.69832E-13 
9.61261E-13 
7.47750E-13 
8«.94928E-14 
-8.65347E-13 
-1* 94031E-12 
-2.94427E-12 
-3.67819E-12 
— 3» 93904E-12 
-2* 22342E-12 
3c 82983E-12 
1*58109E-11 
3 * 52487E-11 
6.35933E-11 










































, 





































60 


TABLE 6. - VARIANCES AND COVARIANCES AT EVEN INCREMENTS OF PRESSURE 


RUN HQ. hE“0-2 


PRESSURE, ATM « 

1 * 000E-00 

2 * OOGE-QG 
5.000E-00 
1.GOGEEQ1 
2•5QGEC01 
5 « OOOEGG1 
7 o 500E SOI 
1 * 000EC02 
1 * 250EC02 
1.50GEC02 
2•000EC02 
2.50GEEG2 
3.00QEE02 
3.500EE02 
4#0006802 
4.500EE02 
5.000EC02 
6* OOOE C02 
7.000EE02 
8.00QEC02 
9.000ES02 
1 * OOOE £03 


S2P 

9.95049E-08 
2.65831E-07 
8•40598E-07 
1•68501E-06 
2 • 81845E-06 
2 « 7 8692E —06 
3.18659E-06 
4* 49544E—06 
6.07452E-06 
7* 21926E—06 
7•13161E—06 
5.88843E-Q6 
8 « 78845E-06 
2.040686-05 
4.10249E-05 
6.51Q29E-05 
8« 23239E-05 
5.67960E-05 
1« 53375E-06 
4.06824E-04 
2.71044E-03 
9.91610E-03 


S28P 

2 o 362036-10 
3* 82Q34E-1Q 
6c 62358E-10 
9 0 00285E-10 
9o 80918E—10 
4. 38016E-10 
-2.73125E-1Q 
-9o 071186-10 
“1o 37272E-09 
-1o 63315E-09 
-1c 5347 5E-09 
-6.922326-10 
6o99102E“10 
2 o 39617E-09 
4«12970E-Q9 
5•61592E-Q9 
6o 56318E-09 
5o 65843E-09 
— 9o 464536—10 
-1o 55720E—08 
“4o Q4593E-08 
-7o 774236-08 


S2CP 

-1•52400E-13 
-2.45627E-13 
-4.22522E-13 
-5* 67722E-13 
-5 c 92770E—13 
-2* 041516-13 
2.79354E-13 
6* 98532E-13 
9.95155E-13 
1.14798E-12 
1c 01813E-12 
3.77899E-13 
-6.33702E-13 
-1.84511E-12 
-3.06767E-12 
-4.10335E-12 
-4.74907E-12 
-4o 04880E-12 
6.729066-13 
lo10250E-11 
2.85601E-11 
5o 47555E-11 










































































































































































61 


TABLE 6.- VARI ANf.FS 


PRESSURE, ATM* 

l.OQGE-OG 
2 * GOGE—00 
5 * OGOE-QQ 
1.G00EE01 
2.500EE01 
5•00GEE01 
7•500EEG1 
1•0Q0ECG2 
1.250EE02 
1.500EE02 
2* 000ECG2 
2•500EE02 
3* 000EE02 
3•5GGEE02 
4.QGGEE02 
4.50QEE02 
5* G00EE02 
6.00GEE02 
7.000ESG2 
8.00QEE02 
9.G00EC02 
1 * 00GEEG3 


NP .COVARIANCE 


AT EVEN INCREMENTS OF PRESSURE 


RUN NO* HE—0-3 


S2P 

1*231L2E-Q7 
3* 29369E-07 
1•04460E-06 
2.10172E-06 
3.54524E-06 
3.51873E-06 
3.97544E-06 
5.56874E-06 
7.54629E-06 
9* 03797E-06 
9.10348E—06 
7.45861E-06 

1 * 042 79E-05 

2 * 38365E-05 
4.86554E—05 
7 * 89406E-05 

1 * G27G7E-04 
8•02312E-05 
3* 09G30E—08 
3* 74376E—04 

2 * 77004E-03 
1*G5137E-G2 


S2BP 

2 * 87476E—10 
4o 65343E—10 
8.08234E-10 
1.10129E-09 

1 * 20992E-09 
5« 61070E-10 

-3* 01240E-10 
“1«07795£—09 
-1.65695E-09 
-1o 99455E—09 
-1o 92047E-09 
-9« 48426E-10 
6« 99089E-10 

2 * 73918E—09 
4.85710E-09 
6o 72Q42E—09 
7o 98704E-09 
7o 34186E-09 
lo46772£—10 

-1 * 63260E-08 
-4o47113E-08 
~8o75182E-08 


S2CP 

-1 •82392E-13 
-2 ® 94213E-13 
-5.07034E-13 
- 6 * 83G69E-13 
-7*19774E-i3 
-2* 62065E-13 
3.15Q70E-13 
8 * 20778E-13 
1 * 1846IE-12 
1.38024E-12 
1.25786E-12 
5.27721E-13 
-6.52553E-13 
-2.08645E-12 
-3.55703E-12 
-4.83609E-12 
-5-68935E-12 
-5c16941E—12 
-1 * 02665E-13 
1.13709E-11 
3.10462E-11 
6c 06315E-11 






























































■ 









































■ . 


































62 


TABLE 6.- VARIANCES AND COVARIANCES AT EVEN INCREMENTS OF PRESSURE 


RUN NO* HE—0-4 


PRESSURE, ATM. 

l.OOOE-OG 
2.000E-00 
5 • OOOE-GO 
I•OOGESOI 
2.50GE8G1 
5•000ES01 
7.50GESG1 
1.GQGESG2 
1.25GEGG2 
l.500ES02 
2.000ES02 
2.500ESG2 
3.000EG02 
3.500E602 
4.000ES02 
4.50QESG2 
5.000ES02 
6«00GESQ2 
7 « QG0E&Q2 
8.000ES02 
9.000ES02 
I•000E&G3 


S2P 

I.00947E-07 
2* 70229E—07 
8.58072E-07 
1.72902E-06 
2.92659E-06 
2•90944E—06 
3*27149E-06 
4.56893E-06 
6.19773E-G6 
7•44537E-06 
7.55811E-06 
6.18019E-06 
8.41929E-06 
1.90995E-05 
3.92142E-05 
6.41835E—05 
8•44427E-05 
6.90575E—05 
4.90871E-07 
2 * 70513E—04 
2.1005 8E-03 
8.10367E-03 


S2BP 

2.34127E-10 
3 o 79112E—10 
6•58937E-10 
8.98767E-10 
9.90695E—10 
4.66189E-1Q 
-2.3501IE—10 
—8.69216E-10 
—1.34474E-09 
-1.62560E-09 
-1.58091E-09 
-8.06653E-10 
5.20103E-10 
2 o17313E—09 
3.90024E-09 
5.43479E-09 
6.50222E-09 
6.12066E-09 
5.25800E-10 
-1 © 24761E—08 
■=3.5005 8E-08 
-6o 90846E—08 


S2CP 

-1.47537E-13 
-2.38070E-13 
-4.10587E-13 
—5.53723E-13 
-5.85617E-13 
-2.17798E-13 
2.48529E-13 
6.58883E—13 
9.56032E-13 
1.11837E-12 
1.03005E-12 
4.51111E-13 
-4.93726E-13 
-1.64832E-12 
-2.84Q01E-12 
-3.88696E-12 
-4.60238E-12 
-4.28157E-12 
—3.65373E-13 
8.63201E-12 
2.41455E-11 
4.75421E—11 


























































































































































. 













































































63 


TABLE 6.- VARIANCES AND COVARIANCES AT EVEN INCREMENTS OF PRESSURE 


RUN NO. HE-O-5 


PRESSURE, ATH. 

l.OOOE-GO 

2.000E-00 

5.000E-00 

l.OGOEEQl 

2.500EC01 

5•OOOECOl 

7.500EC01 

1.000EC02 

1.250EE02 

1.500EC02 

2.000ECG2 . 

2.500EC02 

3.000EC02 

3.500EC02 

4.000EC02 

4.50QEC02 

5.000EG02 

6.000EC02 

7.000EE02 

8.000EC02 

9.000EG02 

1.000EC03 


S2P 

1.20232E-07 
3.21524E-07 
1.01879E-06 
2•04747E-06 
3.44476E-06 
3.41493E-06 
3.87239E-06 
5.43660E—06 
7.36U1E-06 
8.79534E—06 
8.80563E-06 
7.22867E-06 
1.03148E—05 
2.37096E-05 
4.81795E-05 
7•76454E-05 
1•00156E-04 
7.54254E-05 
8.49343E-08 
4.02371E—04 
2•87665E-03 
1« 07921E-02 


S2BP 

2 o 82162E-10 
4o 56627E-10 
7•9266QE- 10 
1o 07924E-09 
1.18267E-09 
5.42160E-I0 
—3.05246E—10 
-1•06612E-09 
-1.63072E-09 
-1.95658E-09 
-1.86920E-09 
-8.98676E-10 
7.32790E-10 
2•74362E—09 
4.82G94E-09 
6.63450E-09 
7o84455E-09 
7o 07549E—09 
-2.41792E-10 
-1 © 68169E—08 
-4.52682E-08 
-8© 80911E-Q8 


S2CP 

-1.79962E-13 
-2.90219E—13 
—4.99867E—13 
-6.72869E-13 
-7.07028E-13 
-2.53129E-13 
3.I6825E-13 
8.14606E-13 
1.17093E-12 
1.36008E-12 
1.22920E-12 
4.97595E-13 
-6.76579E-13 
-2•09675E—12 
-3.54618E-12 
-4.79698E-12 
-5.61526E-12 
-5.00696E-12 
1•69992E-13 
1*17728E-11 
3.15948E-11 
6.13436E—11 























































































. 


















































64 


TABLE 6.- VARIANCES AND COVARIANCES AT EVEN INCREMENTS OF PRESSURE 


RUN NO. HE-0-6 


PRESSURE, ATM. 

I*GOOE-OO 
2* OOOE—GO 
5.000E-00 
l.OOOECOl 
2.500EC01 
5.OOOECOl 
7.5GGEEG1 
1.GGGECG2 
1.250EC02 
1.SOOEC02 
24 G0DEC02 
2-. 50GEEG2 
3.0G0EC02 
3.500EC02 

4. QOOEC02 
4.50GECG2 

5. G00ES02 
6* QQQECG2 
7.G0GECG2 
8.00GEEG2 
9.G0GECG2 
I•G0GES03 


S2P 

7.62393E—08 
2*04013E-07 
6*47332E-07 
1.30317E-06 
2.20112E-06 
2.18604E-06 
2•46534E-06 
3.4495GE-06 
4.67632E-06 
5.60719E-06 
5.66464£^*06 
4.63726E—06 
6.4197GE-06 
1•46339E-05 
2.99390E-05 
4.87392E-05 
6•36869E-05 
5.0647GE-G5 
1•02569E—07 
2.21065E-04 
1•66559E—03 
6 o 36111£—03 


S28P 

1 * 77562E-10 
2.87459E—10 
4.99412E-10 
6.80758E-10 
7•48848E—10 
3* 492G7E-10 
-1.83105E-10 
-6.63334E-10 
-1.G2211E-09 
-1.23235E-09 
~1 * 1911IE-09 
-5.957I9E”10 
4*17613E—10 
1« 67536E-09 
2.98432E-09 
4.14034E-09 
4.93329E-09 
4.57693E-09 
2.09829E-10 
-9.84523E-09 
-2.72089E-08 
-5.34255E-08 


S2CP 

-1. 12362E-13 
-1.81272E-13 
-3.12486E-13 
-4.21146E-13 
-4.44395E—13 
-1.63U9E-13 
1.92282E-13 
5.04203E-13 
7*29175E-13 
8.50886E-13 
7 * 78388E-13 
3* 32145E-13 
-3.92142E-13 
-1.274G4E-12 
-2.18072E-12 
-2.97241E-12 
-3.50555E-* 12 
—3* 21458E-12 
-1.46401E-13 
6.83965E-12 
1.88448E-11 
3.69177E-11 













































































































* •> 





















































































































































65 


TABLE 6.- VARIANCES AND COVARIANCES AT EVEN INCREMENTS OF PRESSURE 


RUN NO. HE-O-7 


PRESSURE, ATM. 

I.OOGE-OQ 
2.000E-00 
5.Q00E-00 
l.OOOECOl 
2 • 500EE01 
5•0GG6C01 
7•500E8Q1 
1.0006C02 
1•25GEE02 
1•500EC02 
2.000EC02 
2.500EC02 
3.000EC02 
3.500EE02 
4.000ECG2 
4. 500EC02 
5•G00E602 
6.000EC02 
7.000EC02 
8.00QEE02 
9.000E&02 
1.000E&03 


S2P 

7.396186-08 
1.97898E-07 
6.2779IE-07 
1.26348E-06 
2.13272E-06 
2.II749E-06 
2•39020E-06 
3.34623E-06 
4.53538E-06 
5.43494E-06 
5.48222E-06 
4.48982E-06 
6.24786E-06 
l•42639E-05 
2.91494E-05 
4.73725E-05 
6•17654E-05 
4.86670E-05 
4.88890E-08 
2•20131E-04 
1.64297E-03 
6.25544E-03 


S2BP 

1*724656-10 
2.79191E-10 
4.84982E-10 
6.609626-10 
7.2661 IE-10 
3.37875E—10 
— 1.79325E-10 
-6.4555 IE-10 
-9.93472E-10 
-1.19683E-09 
-1.15450E-09 
-5.73628E-10 
4.12895E-10 
1•63591E—09 
2.907146-09 
4.02767E-09 
4.79274E-09 
4 o 42528E-09 
1.42876E-10 
“9.68927E-09 
-2.66513E—08 
-5 * 22496E-08 


S2CP 

-1.09294E-13 
-1.76312E-13 
— 3* 03893E—13 
-4.09484E-13 
-4.31787E-13 
-1.57840E-13 
I.87940E-i3 
4.91170E-13 
7•09596E-13 
8.27393E-13 
7.55510E-13 
3.19518E-13 
-3.86506E-13 
-1.24519E-12 
-2.12693E-12 
-2.89531E-12 
-3.41026E-12 
-3.112366-12 
-9.98272E-14 
6.74077E-12 
1•84847E—11 
3.61562E-11 






















































































66 


TABLE 6.- VARIANCES AND COVARIANCES AT EVEN INCREMENTS OF PRESSURE 


RUN NO. HE—0-8 


PRESSURE, ATM• 

l.OQOE-OQ 
2•QQOE-OO 
5.000E-00 
1•OOOE&OI 
2•5QGE801 
5 oOOOESOI 
7•500ES01 
1«000ES02 
1.250ES02 
1•500EE02 
2.000ESG2 
2•500E 602 
3.00GESG2 
3.500ES02 
4.OQQE £02 
4.500EE02 
5.Q0GEEG2 
6•000ESG2 
7.000ES02 
8 oOOOE £02 
9.0GGE£Q2 
1.00GE£Q3 


S2P 

1* 08490E—07 
2* 90231E-07 
9.2G334E—07 
1.85133E-06 
3*12145E—06 

3 « 09747E-06 
3. 50187E-06 
4.90739E—06 
6. 64903E-06 
7.95976E-06 
8•00807E-06 
6* 56343E-06 
9.21403E-06 
2.10884E-05 

4 „ 30132E-05 
6 » 97015E-05 
9* 05431E—05 
7.024376-05 
6•23026E-09 
3 o 3670 IE-04 
2.474806-03 
9.37419E-03 


S2BP 

2 o535366—10 
4 o 10386E-10 
7 o12712E— 10 
9.71006E-10 
1o 06627E-09 
4« 933916-10 
—2 o 67327E—10 
—9« 5213 IE-10 
-1.462166-09 
-1.75898E-09 
-1.691086-09 
-8.30789E—10 
6.25032E-10 
2•42620E-09 
4o 29443E-09 
5.93577E-09 
7o 04768E-09 
6.45524E-09 
6.19225E-11 
-1.45475E-08 
-3o 97080E—08 
-7o76456E~08 


S2CP 

-1.61031E-13 
-2.59745E-13 
-4.47588E-13 
-6.02897E-13 
-6.34962E-13 
-2.30457E-13 
2.79198E-13 
7* 25504E-13 
1•04629E-12 
1.218356-12 
1.108546-12 
4.61855E-13 
-5.82080E-13 
-L.84931E-12 
-3.147816-12 
—4.275606-12 
-5.02525E-12 
-4.5498 LE-12 
—4.33589E-14 
1.01427E-11 
2.76010E-11 
5.38484E-I1 



















































. 





















67 


TABLE 6 -~ VARIANCES AND COVARIANCES AT EVEN INCREMENTS OF PRESSURE 


RUN NO. HE—Q—9 


PRESSURE, ATM. 

1.000E-00 
2•Q0QE-00 
5.000E-00 
l.OOOE&Gl 
2.500ESG1 
5.000EE01 
7.500ES01 
1.0G0ESQ2 
1.250ES02 
1•50QES02 
2.000ES02 
2.500ES02 
3.000ES02 
3.500ES02 
4.00GES02 
4.500ES02 
5.000ES02 
6.000ESG2 
7•000ESG2 
8.000ES02 
9.000ES02 
1.000E&03 


S2P 

2.10452E-08 
5•61791E—08 
1.77359E-07 
3•54803E—07 
5.90743E-07 
5.83068E—07 
6.71179E-07 
9.50332E-07 
1.28189E-06 
1•51684E-06 
1•48262E-06 
1.23154E-06 
1.90461E-06 
4.45123E-06 
8.86933E-06 
1.39009E-05 
1.72949E-05 
1•10665E-05 
8.77794E-07 
9.99697E-05 
6.33566E-04 
2 «27538E-03 


S2BP 

5•G4067E—11 
8.14912 E—11 
1.41148E—10 
1.91587E-10 
2.07790E-10 
9«08019E—11 
-6.1247 IE-11 
-1.96031E-10 
-2.94188E-10 
-3.48427E—10 
-3.22367E-10 
-1.37482E-10 
1•63722E-10 
5.28108E-10 
8.96943E-10 
1•20840E-09 
1.39901E-09 
1o16041E—09 
-3 0 32519E—10 
—3 o 58421E-09 
-9.08162E-09 
-lo 72883E-08 


S2CP 

-3.28206E-14 
-5.28734E-14 
-9.08588E-14 
-1.21906E-13 
-1-26638E-13 
-4.22254E-14 
6.20392E-14 
1.51900E-13 
2.14894E-13 
2.46543E-13 
2•15314E-13 
7.39080E-14 
-1.46863E-13 
-4.09167E-13 
-6.71492E—13 
-8.90304E-13 
-1•02G99E-12 
-8.37614E-13 
2.38514E-13 
2.56033E-12 
6.46825E-12 
1•22861E-11 






•• 















. 































■ 




























68 


TABLE 6.“ VARIANCES AMD COVARIANCES AT EVEN INCREMENTS OF PRESSURE 


RUN NO* HE-G-1G 


PRESSURE* ATM* 

UOOOE-OO 
2•000E-00 
5.000E-00 
1® OOQEEGl 
2® 500E&01 
5®0O0EE01 
7*500£&01 
1•000ECG2 
1•25GECG2 
i* 500E602 
2•000EE02 
2.500EE02 
3.GG0EE02 
3.500EE02 
4.00QEE02 
4* 500EE02 
5.0Q0EC02 
6.000E8G2 
7 * OQOE8Q2 
8* 00GECG2 
9.00GEE02 
i•QOQE £03 


S2P 

7* 39614E-08 
1 * 98031E-07 
6.29Q89E-07 

1 ® 2683GE*-06 
2*14937E-06 
2.13807E-06 

2 «400I9E“06 
3.34846E—06 
4.54366E-06 
5.46399E—06 
5*56175E-06 
4® 5453GE—06 
6*13696E-06 
1« 38829E-05 
2•85600E—05 
4.68862E-05 
6.19198E-05 
5.14133E-05 
5.69966E-07 
1 * 89669E-04 
1.49871E-03 
5* 8I553E-03 


S2BP 

Io 71119E—10 
2 * 77118E-10 
4® 81785E—10 
6®57369E-10 
7 ® 25445E-10 
3® 43G93E—10 
— 1o 69132E—10 
-6® 33081E—10 
-9®8i652E~10 
“1®18842E-09 
”1®1597 IE-09 
”5 o 98206E—10 
3® 67723E-10 
1.57376E-09 
2«83663£“09 
3® 96244E-09 
4* 75149E—09 
4® 50809E—09 
4® 83694E-10 
“8 ® 91901E—09 
“2® 52449E~08 
-4o99675E~08 


S2CP 

-1*07591E-13 
—i•73633E-13 
-2.99536E-13 
-4*04108E-13 
-4* 27931E-13 
-1.60316E-13 
1•79625E-13 
4.79203E-13 
6* 9662 IE-13 
8*16048E—13 
7•54329E-13 
3.35076E-13 
-3.5146IE-13 
-1.19212E-12 
—2•G6168E-12 
-2•82822E-12 
-3.35618E-12 
-3*14678E-12 
-3.35384E-13 
6•15741E-12 
1.73746E-11 
3.431G5E-11 

























































































































-- -I 
























































. 
































































- 

. 












































-• 








69 


TABLE 6VARIANCES AND COVARIANCES AT EVEN INCREMENTS OF PRESSURE 


RUN NO. HE-O-11 


PRESSUREf ATM. 

1.000E-00 
2.000E-G0 
5.000E-00 
l.OOOESOl 
2.500EC01 
5.000EC01 « 

7•500E&0I 
1.000EC02 
1.250ECQ2 
1.50GE802 
2.00GEC02 
2.500E802 

3. GGGECG2 
3.50GE8G2 

4. QGGECG2 
4.500E802 
5.00GECG2 
6.00GEC02 
7•000EC02 
8.000E&Q2 
9.000EC02 
1.000EC03 


S2P 

8.77556E-08 
2.34847E-07 
7.45267E-07 
1•50058E-06 
2.53549E-06 
2.5I856E-06 
2.83890E-06 
3.97092E-06 
5.38372E-06 
6.45736E-06 
6.52857E-06 
5.34341E-06 
7.37873E-06 
1.68087E-05 
3.44095E-05 
5.60666E-05 
7.33426E-G5 
5.85836E—05 
1•52691E-07 
2.51655E-04 
1.90486E-G3 
7.28717E-03 


S2BP 

2 © 0422 IE-10 
3.30631E-10 
5 o 74461E—10 
7« 83143E-10 
8.61774E-10 
4© 02475E—10 
-2.09678E-10 
-7.62171E-10 
-I.17518E-09 
-1.41751E-09 
~lo37143E—G9 
—6.88089E-10 
4.76205E-10 
1o 92223E-09 
3.4281QE—09 
4.75936E-09 
5.67456E—09 
5.27668E—09 
2 o 74443E —10 
-lo12606E-08 
“3.11928E-08 
”6.12999E—08 


S2CP 

-1.29160E-13 
-2.0838IE-13 
~3.59248E-13 
-4.84224E-13 
-5.H153E-13 
-1•88040E-13 
2.20457E-13 
5.79137E-13 
8.38002E-13 
9.78273E-13 
8.96G90E-13 
3.83879E-13 
-4.47910E-I3 
-1.46130E-12 
-2.50386E-I2 
—3.41509E—12 
-4.03Q19E-12 
-3.704Q5E—12 
-1.91380E-13 
7•81866E-12 
2.I5922E-I1 
4.23356E-11 
















• 

















• 







■ 






















































































70 


TABLE 6.- VARIANCES AND COVARIANCES AT EVEN INCREMENTS OF PRESSURE 


RUN NO. HE—0—12 


PRESSURE, ATM. 

I.OOOE-O0 
2.000E-00 
5.000E-00 
l.000EG01 
2.50GEGG1 
5•00QE6G1 
7.500ES01 
1.000EC02 
1.250EC02 
1.50QEE02 
2.000EC02 
2.500EC02 
3.000EC02 
3.50GEC02 
4.00GECG2 
4.50QEC02 
5.00GEC02 
6.000E&G2 
7•000EC02 
8.000EC02 
9.00QECG2 
I•Q00EC03 


S2P 

6.I9299E-08 
1.65639E-07 
5.25026E-07 
1.05558E-06 
L.77764E-06 
I.76306E-06 
1.99667E-06 
2.80G95E—06 
3.79353E-06 
4.53642E-06 
4.55139E-06 
3.73362E—06 
5.28974E-06 
1« 21362E-05 
2.47012E-05 
3.99026E—05 
5.16278E-05 
3.93850E-05 
8.63799E-09 
2 . 00663E-04 
1.45156E-03 
5 o 46809E-03 


S28P 

1.45069E-I0 
2.34788E—10 
4.07650E-10 
5.55189E-10 
6.08944E—10 
2.80286E—10 
-1.55222E-10 
—5.46699E-10 
-8.37659E-10 
-1.00620E-09 
-9.63919E-10 
—4.67867E-10 
3*. 68403E—10 
1o 40082E-09 
2.4692 5E-09 
3.40456E-09 
4.03278E—09 
3.66180E—09 
-5.52301E-11 
-8.50652E-09 
-2.30337E-08 
—4.49156E-08 


S2CP 

-9.23623E-14 
-1.48963E-13 
-2.56623E-13 
-3.45538E-13 
-3.63442E-13 
-1.30894E-13 
1.6I543E-13 
4.17245E—13 
6.00610E-13 
6.98393E-13 
6.33044E-13 
2.59545E-13 
-3.414Q0E-13 
—1•06938E—12 
-1.81365E-12 
-2.45772E-12 
-2•88201E-12 
-2.58691E-i2 
3.87635E-14 
5.94489E-12 
1.60486E-11 
3.12237E-11 



































































































. 


























































































71 


TABLE 6.- VARIANCES AND COVARIANCES AT EVEN INCREMENTS OF PRESSURE 


RUN NOo HE-0-13 


PRESSURE 9 ATM 

1o OGOE-GG 
2-000E-00 
5* OOQE-OO 
1oOGOEEOl 
2 o 500ES01 
5*00GE£G1 
7* 500ECG1 

1 * OOGE £02 
1®250E £02 
1•500EE02 

2 o 000E£G2 
2® 500E£Q2 
3*GOOE £02 
3•500EC02 
4® 0GGE£G2 
4® 500E £02 

5 ® OOGE £02 

6 ® 000E£02 

7 « 000E £02 

8 ® 000E £02 
9® 000E £02 
1o 0G0E£03 


S2P 

i® 75638E-06 

4® 70415E-06 
1* 49537E-05 
3*01751E-G5 
5*12510E-05 
5*105616-05 
5*71557E-Q5 
7* 9574GE-G5 
1«,G8Q44E—04 
1®3G207E—04 
1 * 33327E-04 
1* G888QE—04 
1 * 43943E-04 
3 * 228706-04 
bo 66325E-04 
1*10Q38E-03 
1® 46467E-03 
1*25751E-03 
2® 98655E-05 
3*98019E—03 
3 * 27777E-02 
1 * 28618E-01 


S2BP 

4oQ5G64E~G9 
6o56098E~09 
1 o 1411 3E~Q8 
1 * 55797E-08 
lo7230i£-08 
8*22873E“09 
”3o 87800E = 09 
-=lo 48750E-08 
-2*3172QE-08 
-2*81394E“08 
-2*76673E~08 
-lo46271E—08 
7* 99243E—09 
3*63571E“08 
6*61885E“08 
9* 29639E-08 
1 *12G29E“07 
1®08171E“07 
1o 69930E-08 
-1« 98325E-07 
“5o73129E-07 
-lo14082E-06 


S2CP 

-2.52996E-12 
-4.08367E-12 
-7•04775E-12 
-9.51424E-12 
—1.00984E-11 
-3.83492E-12 
4*14996E-12 
1.12074E-11 
1*63530E-il 
1 * 92118E-11 
1 * 79005E-11 
8.20849E-12 
-7•77580E-12 
-2.74281E-1L 
-4*7 8438E-1L 
-6.59655E-11 
“7* 86547E-11 
—7•50402E-11 
-1 * 17G90E—11 
1•36056E-10 
3* 91964E-10 
7.7840QE-10 
















. 









































































































































72 


TABLE 6,“ VARIANCES AND COVARIANCES AT EVENINCREMENTS OF PRESSURE 


RUN NO© HE-0-14 


PRESSURE v ATM* 

loOOOE-OO 
2« 000E-00 
5* 000E-00 
1« 000EC01 
2« 5Q0E601 
5»000E£01 
7•500E £01 
1*000E£G2 
1.250E£02 
1* 500E £02 
2 « OOOE £02 
2 * 500££02 
3«000E£02 
3* 500E£02 
4o OOOE £02 
4*500E£02 

5 « 000E£02 

6 * OOOE £02 
7•000E£02 
8*000E£02 
9* G0GE£02 
1o OOOE £03 


S2P 

8 o 027 04E-08 

2« 14678E-* 07 
6o 80371E-07 
1.36766E-06 
2.30229E-06 

2 o 28296E-06 
2*58685E-06 

3 *> 63009E-06 
4«91589E-06 

5 * 87649E—06 
5•89G57E—06 
4*833666-06 
6«86898E—06 
1.57717E-05 
3« 20782E-05 
5o17661E-05 

6 o 68889E—05 
5* 07409E-05 
2o67735E”08 
2 o 637836—04 
1o 89S31E-G3 
7«I 381IE-03 


S2BP 

1o 88178E-10 

3o G4547E-10 
5 o 287246-10 
7c 200Q0E-10 
7 «89410E-10 
3c62730E-10 
”2 «02 2 88E-10 
“7o 09938E-10 
“•lc 08698E—09 
-lo30505E-09 
— 1« 24875E-09 
~6c036836—10 
4c824686-10 
1o82243E—09 
3 *20807E-Q9 
4«41965E“09 
5® 23108E-09 
4o 73608E-09 
“I®10794E-10 
“Id 11296-08 
“3*001326—08 
84726E-08 


S2CP 

-1 •19903E-13 
-L.93373E-13 
-3.33102E-13 
-4o484626—13 
-4*7I500E-13 
-1.69387E-13 
2*102926-13 
5*421156-13 
7.79885E-13 
9.06437E-13 
8* 20598E-13 
3*346376-13 
—4*4641IE-13 
-1•39193E-12 
-2.35788E-12 
— 3 *19277E-12 
“3*741126-12 
“3* 34837E-12 
7* 78209E-14 
7« 77239E-12 
2 * 09277E-11 
4* 06794E-11 














































































■ 






























































73 


TABLE 6.- VARIANCES AND COVARIANCES AT EVEN INCREMENTS OF PRESSURE 


RUN NO« HE-0-15 


PRESSURE 9 ATHo 

1.00GE-00 
2* 000£—00 
5.000E-00 
1«000£EG1 
2«. 500EC01 
5*0Q0E8Q1 
7•500E COI 
1o 00GE&G2 
I«250EGG2 
1.5Q0E802 
2.00QESG2 
2* 500EE02 
3 * 000E £02 
3* 500E802 
4,00QEE02 
4.500EE02 

5 o OOGE £02 

6 * 000E £02 
7.000EC02 
8* 000EC02 
9«000E£02 
I»00G££03 


S2P 

7*52086E-08 
2*01368E-07 
6 * 39680E-G7 

1 * 28963E—06 

2 * 18541E-Q6 
2*I7386E-06 
2 * 44G48E-Q6 
3*40479E~06 
4.62009E-G6 
5•55578E-06 
5.65485E-06 
4*62139E—06 
6* 24060E-06 
1.41177E-05 
2 * 90412E-05 
4* 76725E-05 
6« 29526E-05 
5* 22560E-05 
5 * 76Q47E-07 
1» 9291GE-04 
1 * 52379E-03 
5 * 91175E—03 


S2BP 

1o74025E~10 
2 o 81823E“10 
4o 89959E-10 
6* 68515E-1Q 
7 © 37721E-10 
3 o 48855E-10 
-U72G66E-10 
-6©43875£~10 
-9©98334E-1G 
-I©20857E-09 
~lol7930E~09 
~6o 08194E-10 
3o 74156E-10 
1« 60063E-09 
2* 8848 IE-09 
4« G2954E-09 
4o83172E“09 
4o 58354E-09 
4« 9Q402E-10 
”9* 07136E-09 
— 2© 56717E-08 
~5 * 08076E—08 


S2CP 

-1.09419E-13 

— 1« 76583E-13 
-3•04622E-13 
-4*109656-13 
-4« 35177E~13 
-1.63001E-13 

1•82714E-13 
4* 8737OE—13 
7*084615-13 
8•29893E- 13 
7*67072E-13 
3.40654E-13 

— 3* 57557E-13 
-1 * 21247E-12 
-2.G9671E-12 
-2.87614E-12 
-3.41288E-12 
—3*19947E-12 
-3* 4003 9E-13 

6* 26266E—12 
1« 76686E-11 
3.48878E-11 











































































































































■ 









































74 


TABLE 6.” VARIANCES AND COVARIANCES AT EVEN INCREMENTS OF PRESSURE 


RUN NOo HE“0”16 


PRESSURE* ATM 

1 o OOOE-QG 
2.000E-00 
5.000E-0Q 
1*0Q0E£01 
2o 500E£01 
5•000E CO1 
7<>5Q0E£01 
Io 0GG££Q2 
1o 250EC02 
Io 500E £02 

2 « 000E £02 
2 * 500E£02 
3.000E£02 
3« 500E £02 
4„000E£02 
4* 50QEE02 
5 o 000E£02 
6* 000E £02 
7 « 000E £02 
8o00G££02 
9o00GE£02 
1*000E £03 


S2P 

6.17G67E-Q8 
1*65186E-G7 
5* 24536E-07 
U05697E-06 
1o789I5E—06 

1 o 77875E-06 
2«00G04E“06 

2 o79315E—06 
3.78888E-06 
4 0 55167E-Q6 
4 0 62G76E-06 
3o77828£-06 
5*14676E-06 
lo16759E-05 
2 o 39742E-05 
3•92425E—05 
5.16330E-05 
4o 22335E-05 
3o 00953E-07 
1.65433E—04 
I« 28490E-03 
4.95783E-03 


S2BP 

1o 43G95E-10 
2o 31708E“10 
4«Q2738£=10 
5o49326E“10 
6o05529E“10 
2 o84967E—10 
= 1o43 608E—10 
-5 a 31248E—10 
-“8 o 2 1913E*=10 
= 9o 93597E—10 
-9o 66326E-10 
”4 o 93117E—10 
3o 17826E-10 
1o32824E-09 

2 o 3 8399E —09 

3 © 32211E—09 
3.97474E-09 
3o 74184E—09 
3o21847E“10 

-7o6271G£-09 
-=2o 14026E-G8 
“4o22424E—08 


S2CP 

—9* 01788E-I4 
-la 45516E-13 
— 2 « 50966E-13 
”3 ® 38460E-13 
“3» 57966E-13 
-lo33149E-13 
lo51891E-13 

4 o02726E-13 
5-84371E-13 
6*83619E-13 
6o29662E-13 
2 a75800E-13 

-3* 01742E-13 
-lo00754E-12 
-1.73604E-12 
-2o37612£-12 
“2» 8135 7E“12 
“2«61768E-12 
-2.23662E-13 

5 * 27738E-12 
1® 47636E-11 
2 * 90719E- 11 














































































. 






• 






























































. 


























































































75 


TABLE 6 .— VARIANCES AND COVARIANCES AT EVEN INCREMENTS OF PRESSURE 


RUN NO. HE-0-17 


PRESSURE 9 ATM. 

1.000E-00 
2.000E-00 
5. QG0E-00 
Io 0G0ESG1 
2.500EC01 
5.G00EC01 
7.500EC0I 
1•000EG02 
1.250EEQ2 
1o 500E£02 
2.000EC02 
2 « 500EC02 
3.000EC02 
3.500EC02 
4.000EC02 
4.500EC02 
5.000EE02 
6 .000EC02 
7.000EC02 
8o000EC02 
9®00GE£02 
Io000EEG3 


S2P 

5.80316E-08 
I 0 55214E-Q7 
4.91988E-07 
9.89I73E-Q7 
1» 66588E—06 
1•65226E-06 
1.87109E-06 
2.62470E-06 
3.55487E"06 
4.251I7E-06 
4 0 26559E—06 
3 o 49904E-06 
4.95582E-06 
1.13692E-05 
2.31420E-05 
3.73883E-05 
4.83817E-05 
3o 69322E-05 
7.11219E-09 
1.87728E-04 
1.35880E-03 
5.11968E-03 


S2BP 

lo35926E-10 
2 ©19992E“10 
3o 81964E—10 
5 o 20212E-10 
5 o 70602E-10 

2 o 62682E-10 

“Io453746-I0 
-5 o12192E-10 
-7 o 84845E“10 
-9o 42 805E- 10 
-9c 03298E-10 
-4o 38627E-10 
3o 44842E-10 
1o 31215E“09 

2 o 31327E-09 

3 o18979E-09 
3o77870E“09 
3o 43222E-09 

—4o 85082E-11 
-7o 96395E—09 
-2o 15709E-08 
-4c20675E-08 


S2CP 

-8.65344E-14 
“1.39564E-13 
-2.40433E-13 
-3•23744E-13 
-3.40532E-13 
-Io 22673E-13 
1 o 51309E-1 3 
3.9088 7 E-13 
5.62704E-I3 
60 54346E-13 
5.931961-13 
2.43344E-13 
“3.19616E-13 
“1.00164E-12 
-1 * 69897E-12 
-2.30250E-12 
-2.70022E-12 
-2.42453E-12 
3.40430E-14 
5.56526E-12 
1.50283E-11 
2.92414E-11 

































. 










■ 














































• 



















\ 



















76 


TABLE 6.- VARIANCES AND COVARIANCES AT EVEN INCREMENTS OF PRESSURE 


PRESSURE, ATM. 

1 * OOQE-OO 

2 « OOOE-OO 
5.000E-00 
1 « OOOESOI 
2.500ES01 
5 o OOOE SOI 
7.500EC01 
1•000EC02 
1.250ECQ2 
1.500EE02 
2.000EC02 
2.50GEC02 
3* 00QESO2 
3.50QEE02 
4.000EE02 
4.500ES02 
5* 000EC02 
6.000EE02 
7.000ES02 
8•000EE02 
9.000EC02 
I«000E&Q3 


RUN NO. 


S2P 

4.72049E-08 
1.26353E-07 
4.01I44E-07 
8•08129E—07 
1 •36715£“06 
I•35885E-06 

1 •52916E-06 

2 . 13662E-06 
2•8978IE-06 
3.47940E-06 

3 . 52753E-06 
2.88524E-06 
3.94764E-06 
8.96781E-06 
1 * 83957E-05 
3.00667E-05 
3.94860E-05 
3* 2052IE-05 
1•74178E-07 
1«29384E-04 
9. 96438E-04 
3.83404E-03 


HE—0-18 


S28P 

1o 09589E—10 
io77444E-10 
3o08382E“10 
4o 20555E-10 
4o 63322E-10 
2o17502E-10 
-1.10814E-10 
-4.07565E—10 
-6o 29858E-10 
-7•60876E-10 
-7 o 38745E-10 
-3.74940E-10 
2.47343E—10 
1® 02188E-09 
1e 8303IE-09 
2 « 54747E-09 
3« 04450E—09 
2o 85477E-09 
2 o14418E-10 
-5 © 90666E—09 
~lo65045E-08 
-3 o 2 5292E-08 


S2CP 

-6.91449E-14 
“1 * 11568E-13 
—1*92393E-13 
-2.59420E-13 
— 2.7 4200E-13 
-1.01625E-13 
1.16976E-13 
3.09206E-13 
4.48259E-13 
5* 24033E-13 
4.81810E-13 
2.09544E-13 
-2* 34096E-13 
-7.75719E-13 
-1 * 33417E-12 
-1.82401E-12 
-2 o15746E-12 
-1 * 99938E-12 
-1.49176E-13 
4.09167E-12 
1.13980E-11 
2.24130E-11 









f 






































































■ 




































































































77 


TABLE 6.- VARIANCES 


PRESSURE* ATM* 

1.0Q0E-00 
2 « GGOE-QO 
5 * OOOE—00 
1 * OOGECQ1 
2.500EC01 
5 * OOOE SOI 
7o 500EC01 
1.000E&02 

1 * 250E SQ2 
1o500E £02 

2 * G00EC02 
2•5GQEC02 
3.OOOE £02 

3 . 50GE £02 
4® 000E£02 
4-500E£02 
5•000E£02 
6•OOOE £02 
7•OOOE £02 
8•000EC02 
9.000EC02 
1.000E&03 


AND COVARIANCES AT EVEN INCREMENTS OF PRESSURE 


RUN NO. HE—0- 19 


S2P 

7® 50513E-08 
2.00648E-Q7 
6.35437E—07 
1•27616E-06 
2.14375E-06 
2.12376E-06 
2.41365E-06 
3•39309E-06 
4.59178E-06 
5.47860E-06 
5.46534E-06 
4.49264E-06 
6.48815E-06 
1«49576E-05 
3.03094E—05 
4.86465E-05 
6© 24214E-05 
4.59543E-05 
2.05213E-07 
2.65346E—04 
1.85994E-03 
6o92970E-03 


S28P 

1.76669E-10 

2 o 85 862E-10 
4 ® 96065&-10 
6.75108E-10 
7® 38669E-10 

3 ® 36266E-10 
-1.94687E—10 
-6® 70518E-10 
“lc02263E-09 
-1o 22460E-09 
-1*16444E-Q9 
-5®50719E~10 

4® 75973E-10 
1.73786E-09 

3 o 03759E—09 

4 «16692E-09 
4® 91167E-09 
4© 37860E-09 

-2 o 97933E-10 
-1.08249E-G8 
-2.88515E-08 
-5 ® 59490E-08 


S2CP 

-1®13034E-13 
~1® S2257E-13 
-3.13809E-13 
-4.22211E-13 
-4.42892E-13 
-1 *56947E-13 
2. 01219 E -13 
5.13417E-13 
7.36215E-13 
8 . 5357IE-13 
7 o 67593E-13 
3 o 03946E-13 
-4.37020E-13 
-1 ® 33083E-12 
-2.24035E-12 
-3.02144E-12 
-3.52621E-12 
-3.10787E-12 
2 *10102E-13 
7.60141E-12 
2® 01990E-11 
3.90816E-11 











































' 





. 






















































’ 

















































78 


TABLE 6 .- VARIANCES AND COVARIANCES AT EVEN INCREMENTS OF PRESSURE 


RUN NO* HE-0-20 


PRESSURE 9 ATM * 

L.OOOE-OO 
2 * OOOE—QO 
5.000E-00 
I<, OOOECOI 
2 a 5G0E £01 

5 o OOOE SOI 
7* 500E8G1 
Io000EC02 
1o 250EC02 
1o 50QE £02 

2 * 0G0EG02 
2* 500EC02 
3* 000EG02 

3 * 50GEC02 
4* Q0GESQ2 
4.500EC02 
5.000EE02 

6 «0Q0ECG2 

7 o 000EC02 

8 « 000EC02 
9.000ECG2 
1«00GE£Q3 


S2P 

5 o 78136E-08 
i*54364E-07 
4.87555E-07 
9.75899E-07 
I.62695E-06 
1* 60658E-06 
1« 84582E-06 

2 * 6 1Q89E-Q6 
3.52361E-06 
4*1746 IE-06 
4* G9259E-06 

3 « 39327E-06 
5.19577E-06 
1.21229E-05 
2.42175E-05 
3.80904E-05 
4* 76104E-05 
3*11364E-05 
1« 90255E-06 
2.63469E-04 
1.69268E-03 
6*11G27E-G3 


S2BP 

1 * 38124E-10 

2 o 2332 9E-10 
3* 86929E-10 
5* 254Q1E-1Q 
5* 7Q576E-1Q 
2* 50878E”10 

-1 * 65544E—10 
-5* 35277E“10 
-8•0517 8 E~10 
“9 c 55170E—10 
-80 87335E-10 
“3* 84627E-10 
4« 37453E-10 

1 * 43427E-09 

2 o 44589E-09 
3* 30387E-09 
3o83 521E-G9 
3*21690E-09 

-80 Q9158E-10 
“9*61817E-09 
-2o 45377E—08 
-4o68321E-08 


S2CP 

~8» 97060E-14 
~1 * 44533E-I 3 
“2 * 48441£-13 
"3* 33472E-13 
"3* 46919E-13 
-1.16755E-13 
1.68117E-13 
4.14G47E-13 
5•869G9E-13 
6.74386E-I3 
5 « 91544E-13 
2*077596-13 
— 3* 93432E-13 
“1•10931E- 12 
-1» 82709E-12 
-2.42848E-12 
-2o 79224E-12 
-2•31635E— 1 2 
5.78968E-13 
6.85348E-12 
1 * 74329E-11 
3*31983E—11 







































































. 







































































79 


TABLE 6.- VARIANCES AND COVARIANCES AT EVEN INCREMENTS OF PRESSURE 


RUN NO. HE-0-21 


PRESSURE, ATH® 

l.OOOE-OQ 
2.000E-00 
5.000E-GQ 
1® OOOEEOl 
2.5G0EE01 
5 « OOOE £01 
7.5Q0E £01 
1 * 0G0EEG2 
1.250EE02 
1.50GEEQ2 
2.00QEEG2 
2.500E&G2 
3.000EEG2 
3.5Q0EE02 
4•OOOEEQ2 
4.500EE02 
5.000EE02 
6.000EE02 
7.000EEG2 
8 ® 000EE02 
9.000EE02 
1.000EE03 


S2P 

7o 57172E-08 
2•04373E—07 
6.60G81E-07 
1o3585 5E-Q6 
2•41364E-06 
2 « 46862E-G6 
2 « 6G954E-06 
3.46389E-06 
4.72750E-06 
5•89806E-06 
6•67564E-06 
5.60520E-06 
5.53286E-06 
1.01897E-05 
2.19110E-05 
4.00534E-05 
6.04790E-05 
7 ® 97279E-05 
3.60952E-05 
8.99218E-06 
4® 01034E-04 
2 o 20156E-03 


S2BP 

1o 5932 IE-10 
2o 59195E—10 
4® 5511IE—10 
6•29534E“10 
7® 262G6E-10 
4.Q9541E—10 
-5.39556E-11 
-4® 97628E“10 
”8 o56096E—10 
-lo10107E-09 
-1« 21848E—09 
-8.63176E-10 
-1®18935E-1G 
8o 97473E—10 
2.05168E-09 
3.19933E-09 
4®19025E—09 
5® 08738E—09 
3.50734E-09 
-1.77409E—09 
-lo19469E-08 
-2 o 81515E-08 


S2CP 

-9.0881IE-14 
-1o47358E-13 
-2.56837E-13 
-3 ®51538E-13 
-3.90868E-13 
-1.86848E-13 
9.39813E-14 
3 0 55849E—13 
5.61623E-13 
6.95653E-13 
7.32798E-13 
4.8Q810E-13 
-5.99357E-15 
“6.54215E-13 
-1.38029E—12 
“2® 09492E-12 
-=2o 70549E- 12 
-3.23632E—12 
-2.21349E-12 
1.11399E-12 
7•47540E-12 
1.75689E-11 
































































* 




- 









80 


TABLE 6. - VARIANCES 


PRESSURE* ATM• 

lcOOOE-OO 
2*OOQE-GO 
5.0G0E-00 
l.OOOECOl 
2* 500EE0I 
5.QG0EC01 
7.500EC01 

1 * 0G0ECG2 
1.250EC02 
1•500E £02 

2 o 000EC02 
2.500EC02 
3.000EC02 
3* 500EC02 

4 « 000EC02 
4* 500EC02 

5 o 000E £02 

6 . 000E £02 
7o 000E£G2 
8® 000E£02 
9®000E£02 
1 o 0QQE£Q3 


AND COVARIANCES AT EVEN INCREMENTS OF PRESSURE 


RUN NO. HE-Q-22 


S2P 

2.77237E-08 
7•28477E-08 
2•22554E-07 
4® 2716IE-07 
6o 48232E-07 
6o30558E-07 
8®35819E-07 
1.23201E-06 
1o56584E“06 
1•67330E-06 
i«36758E-06 
1® 72691E—06 
4® 43490E-06 
9.62023E-06 
1.50965E-05 
1.70859E-05 
1o25782E-05 
1.67496E-06 
1o66873E—04 
1.12420E-Q3 
4.25559E-03 
Io21054E-02 


S2BP 

7 c 90705E—11 
U26684E-10 
2 «15107E-10 
2® 83836E-10 
2 o78786E-10 
6o 34594E—11 
-1.78790E-10 
-3.68048E-10 
-4o78172E“10 
-5oQ2718E—10 
-3 o 12287E—10 
1.27772E-10 
7.G4888E-1G 
lo28945E-09 
1o74317E-09 
1.92 32 5E“09 
1o 68480E-09 
—6o28724E-10 
-6o34921E“09 
-1® 65971E-08 
-3o 24456E-08 
-5.49086E-08 


S2CP 

“6®12064E-14 
“9.76916E-14 
-1.64440E—13 
-2.14130E-13 
-1.99138E-13 
-1.78295E-14 
1.77441E-13 
3® 24723E—13 
4® 04350E-13 
4®12146E- 1 3 
2•29350E-13 
-1.57187E-13 
“6.51832E-13 
-1.14559E-12 
-1.52271E-12 
-1 ®66393E-12 
”1® 44848E-12 
5® 36295E- 1 3 
5 « 38992E-12 
1.40437E-11 
2« 73891E-11 
4.62678E-11 
















• 

t 




















■ ■ 




■ 





• 
































• 












• 

















. 





















81 


TABLE 7.- COMPRESSIBILITY FACTORS AND STANDARD ERRORS AT EVEN 



INCREMENTS OF PRESSURE 



RUN NO. HE-O-l 


PRESSURE, ATM. 

Z 

' SZ 

1.0Q0E-00 

1*0005278182E-00 

8.855946-07 

2.OOOE-OO 

1.0010555406E-0G 

1.717486-06 

5.0006-00 

1.00263813326-00 

4.115526-06 

l.OOOESOl 

1.0052738719E-00 

7.9582IE-06 

2.5006801 

1.01316672076-00 

1.896216-05 

5,0006601 

1.0262735773E-00 

3.638496-05 

7.500E801 

1*0393205700E-00 

5.305046-05 

1 * G00E802 

1.05230769866-00 

6.90955E-05 

1,2 5 0EE02 

1.0652349633E-00 

8.45679E-0S 

1.500E802 

1.0781023639E—00 

9.948276-05 

2.000E802 

1.1G36575730E-00 

1.276306-04 

2.500EG02 

1.12897332616-00 

1.53459E-04 

3.0006802 

1.1540496231E-00 

1.76832E-04 

3.500E602 

1.1788864640E-00 

1.97597E-04 

4.0O0E802 

1.20348384886-00 

2.15594E-04 

4.500E602 

1.22784177766-00 

2.30666E-04 

5.0006802 

1.25196025026-00 

2.42664E-04 

6.000E802 

1.29947882736-00 

2.569006-04 

7.0006802 

1.34603958016-00 

2.574166-04 

8.000E802 

1.3916425086E-00 

2.43773: -04 

9.000E802 

1.43628761276-00 

2.16457 r-Q4 

1.0006803 

1.4799748925E-00 

1.7 8349E-04 




















































• 













































82 


TABLE 7. - COMPRESSIBILITY FACTORS AND STANDARD ERRORS AT EVEN 

INCREMENTS OF PRESSURE 


RUN NO. HE-0-2 


PRESSURE* ATM. 

Z 

SZ 

1.OQOE-O0 

1.0005270514E-00 

9.63911E-07 

2.000E-00 

I.00105400896-00 

1.86686E-06 

5.OOOE-O0 

1.0026343183E~GO 

4.465 28E-Q6 

1 .OOOECOl 

1.0052662900E-00 

8.62282E-06 

2.500EE01 

1.0131481253E-00 

2.05146E-05 

5.OOOECOl 

1.0262375844E-00 

3.93439E-05 

7.500EE01 

1.0392683773E—00 

5.73809E-05 

1 .000EC02 

1.052240504OE-00 

7.47850E-05 

I.250EE02 

1.0651539645E-00 

9.16142E-05 

I * 500EC02 

1.0780087587E“00 

1.07889E-04 

2•000ECQ2 

1.1035423485E-00 

1.387 8IE-04 

2.500EC02 

1.1288412733E-00 

1.67397E—04 

3.000EC02 

1.1539055333E-00 

1.93609E-04 

3.500EC02 

1. 1787351284E-00 

2.17266E-04 

4.000EC02 

1.2033300586E-00 

2.38208E-04 

4.500E&02 

lo2276903238E-00 

2.56275E-04 

5.000EE02 

1.2518159242E-00 

2.71314E-04 

6•0006C02 

i.299363130300 

2.91739E-04 

7.000EC02 

1.3459716767E—00 

2.98496E-04 

8 .000EC02 

1.3916415636E-00 

2.90934E-04 

9.000EC02 

1«4363727908E-00 

2.69003E-04 

1.000E&03 

1.4801653585E—00 

2.33937E-04 





















' 



























































. 















































































83 


TABLE 7- COMPRESS IBILITY FACTORS AND STANDARD ERRORS AT EV EN 

INCREMENTS OF PRESSURE -- 


RUN NO. HE-0-3 


PRESSURE, ATM. 


Z 


SZ 


1.000E-00 
2.000E-00 
5.000E-00 
l.OOOESOl 
2.500ES01 
5.OGOECOl 
7.500EC01 
1 •000EC02 
I.250EE02 
1.500EE02 
2 .000EC02 
2.500EC02 
3.QQ0EC02 
3.500EC02 
4.000EC02 
4.500EC02 
5•000EC02 
6 .000EC02 
7.000EC02 
8 .000EE02 
9.000ECQ2 
1 * 000EG03 


1.0005276588E-00 
1.0010552229E-GO 
1.0026373465 E-00 
1.0052723235E-00 
1.0131630373E-00 
1.0262668364E— 00 
1.0393113972E-00 
1.0522967197E-CO 
1.0652228039E-00 
1.0780896499E-00 
1.1036456271E-00 
1.12896465126-00 
1.154G467223E-Q0 
1.1788918403E-00 
1*2035000052E“00 
1.2278712170E-0Q 
1.2520054757E-00 
1.2995631340E—00 
1.3461729800E-00 
1.3918350137E-00 
1•436549235IE-00 
I.4803156442E-00 


1.05758E-06 
2.04752E—06 
4.89493E-06 
9.44892E-06 
2.24701E-05 
4.30866E-05 
6.28415E-05 
8•19129E-G5 
1.00365E-04 
1.18224E-04 
1.52167E-04 
1•8 3675E-04 
2.12614E-04 
2o 38822E-04 
2.62127E-Q4 
2. 82357E-04 
2.99346E-04 
3.229856-04 
3.31965E-04 
3.25547E-04 
3.035846-04 
2 o 67134E-04 














. 








. 





























' 












































84 


TABLE 7. - COMPRESSIBILITY FACTORS AND STANDARD ERROR S AT EVEN 

INCREMENTS OF PRESSURE -— 


RUN NO, HE-O-4 


PRESSURE f ATM * 


Z 


SZ 


1 .OOOE-OO 

1•0005271219E-00 

2.GOGE-Q0 

1*0010541503E-00 

5*OOOE-OO 

1•0G26346736E-00 

1.G00EL01 

1.G052670067E-0C 

2.500E&01 

1.0131499623E-00 

5.000ES01 

1.0262414097E-00 

7.500EC01 

1•0392743422E—00 

1.000EE02 

1.0522487597E-00 

1.250ES02 

1 „0651646624E—00 

1.500EC02 

1.Q780220501E-00 

2* 000EC02 

1*1035612807E-00 

2•5QQE802 

1•1288664516E-0Q 

3 * Q00ELG2 

1*1539375628E-00 

3* 500EE02 

1.1787746143E-00 

4* OOQE 802 

1-2033776061E-00 

4.500E802 

1.2277465382E-00 

5 * G0OE802 

1.2518814105E-00 

6•000E802 

1.2994489762E-G0 

7.000E802 

1 * 3460803029E-00 

8.000E802 

1.3917753909E-G0 

9.000E802 

1 * 4365342400E-00 

1 *000E803 

1.4803568503E-00 


9o 5205IE-07 
1.84300E-06 
4.40531E-06 
8 * 50280E-Q6 
2 o 021766-05 
3.87657E-05 
5.65408E-05 
7.37043E-05 
9*03152E-05 
1.06395E-04 
1.36974E-04 
1.65383E-04 
1*915G3E—Q4 
2•15190E-04 
2« 36292E-04 
2* 54653E-04 
2.7G125E-04 
2*9185 IE-04 
3.00495E-04 
2* 95380E-04 
2 * 763 37E-04 
2 « 44217E-04 





















>■ 







































■ 




N. 






























. 












. 




























































85 


TABLE 7.- COMPRESS 


PRESSURE, ATM 

I* OGGE-O0 
2.000E-00 
5 * 000E-00 
1. OOOEEOl 

2 .500EE01 
5.OQOEEO1 
7•500EE01 
1.000EE02 
1 * 250EE02 
i.5GGEE02 
2•000EC02 
2•500EC02 

3 * 000EE02 
3.500EC02 
4.000E&02 

4 .500EC02 

5 * 00QECQ2 
6•G00E&Q2 
7,0GGE£02 
8.000E&02 
9.000EE02 
1 * GQQEC03 


BILiTY FACTORS AND STANDARD ERRORS AT EVEN 

INCREMENTS OF PRESSURE 


RUN NO. HE—0-5 


Z 


SZ 


1.000526834 OE- 00 
1•0010535747E-00 
1.0026332369E-00 
1.0052641404E-00 
1*0131428510E-00 
1.0262273681E-00 
1*0392535512E-00 
1*0522214005E-00 
1*0651309158E—00 
1.0779820972E-00 
1.1035094582E-00 
’.1288034836E-00 
i*1538641733E-00 
1.1786915272E-00 
1.2032855455E-00 
1.2276462281E-00 
1.2517735751E-00 
1.2993282618E-00 
1.3459496059E-00 
1*391637607IE-00 
1.4363922657E-GO 
1.4802135815£-00 


1.04930::-;,! 
2.03179E-06 
4.85829E-06 
9.37963E-06 
2.23094E-0 
4.2 7 818 E - C 
6.2397 OE—05 
8.13305E-05 
9.96463E-05 
1. 17368E-04 
1.51036E-04 
1.82269E-04 
2.10932E-04 
2.36862E-04 
2.59888E-04 
2.79839E-04 
2.96549E-C4 
3.19631E-04 
5•28058E—04 
3.21101E-04 
2.98634E-04 
2.61789E-04 




























. 































































































































86 


TABLE 7. - COMPRESS 


PRESSURE, ATM 

1 * OGOE-GG 
2.OQOE-O0 
5.000E-00 

1 * OOOEEOl 

2 * 500EC01 
5.OOOEEOl 
7.500E8Q1 
1 * 000E802 
1 * 250E802 
1•500E002 
2. 0G0E802 
2.5Q0EG02 

3 . Q0QE8O2 
3.500E802 
4.00GES02 
4.500EE02 
5 * G00E602 
6.0G0E&02 
7.G0QE8Q2 
8*00GE&02 
9.000E8Q2 
1 •000EC03 


BILiTV FACTORS AND STANDARD E RRORS AT EVEN 

INCREMENTS OF PRESSURE -- 


RUN NO. HE-0-6 


Z 


SZ 


1.0005273614E-00 
1.0010546288E-00 
1.G026358665E-00 
1.0052693812E-00 
1*0131558144E-00 
1 * 02 62 52832 9E-00 
1 *0392910556E—00 
1.0522704825E-00 
1*0651911136E-00 
1.07 80 52 9488 E-00 
1 * 1036002317E-00 
1.1289123313E-00 
1.1539892475E-00 
1*1788309803E-00 
1.2034375299E-00 
1*227808896OE-00 
1.2519450788E-00 
1 * 2995118944E-GO 
1*3461379766E-00 
1*3918233253E-00 
1*4365679407E-00 
1*4803718227E-00 


8.30354E-07 
1.60753E-06 
3.842 87E-06 
7.41778E-06 
1.76392E-05 
3 * 38228 E- 05 
4.9331 0E-05 
6 .43036E-05 
7.87920E-05 
9.28154E-05 
1.19473E-04 
1.44228E-04 
1•66973E-04 
1.87582E-04 
2•059218-04 
2*21856E-04 
2.35255E-04 
2.53965E-04 
2•61203E-04 
2* 56384E-04 
2•39377E-04 
2*10980E-04 
















































































































. 

. 




































































87 


TABLE 7. - COMPRESSIBILITY FACTORS AND STANPAftP ERRORS AT EVEN 



INCREMENTS OF PRESSURE 



RUN NO. HE-G-7 


PRESSURE, ATM* 

Z 

SZ 

1* 0GGE-00 

1* 000526681IE—GO 

8.18516E—07 

2.000E-00 

1*0010532689£-00 

1.5 8471£—06 

5* 000E-00 

1•0026324726E-00 

3.7 8862E-06 

i•GGOECQ1 

1 * 005262613OE—00 

7.31354E-06 

2.500EC01 

1•0131390400E—00 

1.73927E-05 

5•OGGECOl 

1.0262197717£-00 

3.33514E-05 

7.5G0EE01 

1.0392421952E-00 

4.86437E-05 

I * 00CEC02 

1.0522063105E-00 

6.34072E-05 

1 * 250EE02 

1.0651121175£-00 

7.78925E-05 

1•500EC02 

1.0779596162£-00 

9.15181£-05 

2* 000ES02 

1«1034796888E-00 

1.17797E-04 

2•5GQEEQ2 

1.1287665284E-00 

1.42195E-04 

3 * 000EC02 

1.1538201349E—00 

1.64607E-04 

3* 500EE02 

1.1786405084E-00 

1.84909E-04 

4* 0GGEE02 

1•2032276489E-00 

2.02969E-04 

4.50GEE02 

1*2275815562E-GG 

2.18652E-04 

5•000EE02 

1.2517022306E—00 

2.31831E-04 

6* 000EC02 

1.2992438801E-00 

2 * 50198E-04 

7.000EEG2 

1.3458525974E-00 

2.57232E-04 

8* 000EC02 

1.3915283825E-00 

2.52357E-04 

9.000E802 

1*4362712353E-00 

2.35447E-04 

1.0G0E&G3 

1.4800811560E-00 

2.07303E-04 





































































88 


TABLE 7. - COMPRESSIBILITY FACTORS AND STANDARD ERRORS AT EVEN 

INCREMENTS OF PRESSURE 


RUN NO. HE-0-8 


PRESSURE, ATM. 

Z 

SZ 

1.0006-00 

1.0GQ5265G82E—00 

9.931176-07 

2.000E-00 

1.0010529235E-00 

1.92286E-06 

5•0006-00 

1.0026316126E-00 

4.59738E—06 

1•OOOECOl 

1.0052609039E-00 

8.87527E-06 

2.50068G1 

1.0131348505E-00 

2.11081E-05 

5.OOQESOl 

1.0262116697E-00 

4.04770E-05 

7•500E801 

1.0392304577E-00 

5•90364E-05 

1•OOGE802 

1.0521912145E-O0 

7.69529E-05 

1* 250E802 

1•0650939401£—00 

9.42875E-05 

1.50GE802 

L.07793863A4E-00 

1.11062E-04 

2.000E802 

1.1034539293£-00 

1.42943E-04 

2•500E802 

1.1287370992E-00 

1•725326-04 

3.000E802 

1•1537881442E-00 

1.99704E-04 

3.500E602 

1.1786070642E-00 

2.24307E-04 

4.000E802 

1.2031938592E-00 

2.46179E-04 

4.5GGE802 

1•2275485293E-00 

2.65158E-04 

5.G00E802 

1.2516710745E~00 

2.81088E-04 

6.0006802 

1.2992197898E-00 

3.03222E-04 

7.00GE802 

1•3458400054E-00 

3.11562E-04 

8.000E802 

1.3915317211E-00 

3.05409E-04 

9.00GE802 

1.4362949369E-00 

2.84621E-04 

1.000E8G3 

1.4801296530E—00 

2.50201E-04 



















































. 








. 





































/ 

















































89 


TABLE 7. - COMPRESSIBILITY FACTORS AND STANDARD ERRORS AT EVEN 



INCREMENTS OF PRESSURE 



RUN NO. HE-G-9 


PRESSURE, ATM, 

Z 

SZ 

l.GQOE-GO 

I•0005268877E-GO 

4.46651£—07 

2 * OOQE-OQ 

1.GQ1G536816E-0G 

8•6522GE-07 

5•OGOfc-OO 

I.0026335G04E—GO 

2.Q70G3E-Q6 

1,OOGE&Ol 

1.0G52646548E-QG 

3.99819E-06 

2,500ES0I 

1.0131440416E—00 

9.51426E-06 

5,OQOEEOl 

1.0262294318 £-00 

1.82484E-05 

7.5G0ESG1 

1.0392561707E-00 

2.66137E-05 

I * G00ESG2 

1*0522242582E - 00 

3.46832E-05 

1.250ES02 

1.0651336943E—00 

4.24834E-05 

1•500E&02 

1 • 077984479OE-00 

5.GQ237E-05 

2.Q00ES02 

1•103510G944E-Q0 

6.43259E-05 

2* 500ES02 

1.1288011042E-00 

7.75585E-05 

3.000ES02 

1.1538575086E~00 

8•96613E-05 

3.50GESG2 

1.1786793074E-00 

1•0Q563E-04 

4.000E602 

1.2G32665008E-00 

1.101896-04 

4.500EE02 

1.2276190886E~00 

1.18465E-04 

5.000ES02 

1.2517370710E-00 

1.25319E-Q4 

6,OOOES02 

1.2992692191E—00 

1•34495E-04 

7.G0GES02 

1•3458629453E-00 

1.37262E-04 

8.000ES02 

1.3915182495£-00 

1.33324E-04 

9,0G0EE02 

1•4362351316E—00 

1•22684E-04 

I.000ES03 

1.48GO135918E-00 

1.05992E-04 







































































/ 





































■ 

■ 




































































































































90 


TABLE 7.- COMPRESSIBILITY FACTORS AND STANDARD ERRORS AT EVEN 

INCREMENTS OF PRESSURE 


RUN NO. HE-0-10 


PRESSURE, ATM. 

1.000E-00 
2.OOGE-OO 
5.OQOE-OG 
1•QOQESGI 
2.500ES01 
5•QQQES01 
7.50OES0I 
1 * 000ES02 
1.250EEG2 
1.5Q0ES02 
2.000E&02 
2.500EE02 
3.000EE02 
3.500ES02 
4.OOQEE02 
4.500E8G2 
5.000EC02 
6•000ES02 
7 * 000ES02 
8* 000E&02 
9.000EC02 
1.000E&03 


Z 

1•0005263313E-00 
1.0010525699E-00 
1.0026307296£-00 
1.0052591419E-00 
1.0131304743E—00 
1.0262030140E-00 
1.0392176191E-00 
1.0521742896E-00 
1.0650730254E-00 
1.0779138266E—00 
1.1034216250E—00 
1* 1286976848E-00 
1•1537420061E-00 
1.1785545889E-00 
1.2031354331E-00 
1.2274845387E-00 
1.2516019057E-00 
1.2991414242E-00 
1.3457539883E-00 
1.3914395983E-00 
1.4361982540E-00 
1.4800299555E-00 


SZ 

8.13045E-07 
1.57389E-06 
3.76202E-06 
7.26112E-06 
1•72651E-05 
3.31047E-05 
4•82850E—05 
6.29437E-05 
7 * 71315E-05 
9.08673E—05 
1.16991E-04 
1.41268E-04 
1.63597E-04 
1.838558-04 
2.0191IE-04 
2.17636E-04 
2.30901E-04 
2.49584E-04 
2.57126E-04 
2.52944E-04 
2.36883E-04 
2•09641E-04 





































































































91 


TABLE 


7. - COMPRESSIBILITY FACTORS AND STANDARD ERRORS AT EVEN 

INCREMENTS OF PRESSURE 


RUN NO. HE—0-11 


PRESSURE, ATM. 


SZ 


1.OOGE-GO 

l•0005265339E—00 

8.90040E-07 

2.000E-00 

1•0010529749E—00 

1.72313E-06 

5.OOOE-OO 

1.0026317394E—00 

4.11935E-06 

l.OOOEfiOl 

1.0052611528E-00 

7.95171E-06 

2.500ES01 

1.0131354361E-00 

1.89G96E-05 

5.00QEE01 

1.0262127194E-00 

3.62597E-05 

7.50GEEG1 

1•0392318496E-00 

5•2 8859E—05 

1.0Q0EC02 

1.0521928269E-00 

6.89381E-05 

1.250ES02 

1.0650956513E-00 

8.44714E—05 

1.500EE02 

1•07794Q3227 E—00 

9•95062E-05 

2* 000EC02 

1.1034552067E-00 

1•28088E-04 

2.500EC02 

1.1287374789E-00 

1.54630E-04 

3.000EE02 

1.1537871392E-00 

1•79019E-04 

3.500EC02 

1.1786041877E-00 

2.01121E-04 

4.00QEE02 

1•2031886245E-00 

2.20792E-04 

4.500EE02 

1•2275404494E-00 

2.37887E-04 

5•000EC02 

1.2516596625E—00 

2.52266E-04 

6.000EC02 

1.2992002533E-00 

2.72361E-04 

7.000EE02 

1« 3458103968E-00 

2.80165E-04 

8•000EC02 

1.3914900931E-00 

2.75048E-04 

9.0QGEC02 

1.4362393422E-00 

2.56863E-04 

1•000EC03 

1•4800581440E-00 

2•26454E-04 


















































/ 

























' 










. 









































































































92 


TABLE 7. - C QH ERESSJLBILI TY F ..AC TQ RS.. A MP .S. TAN D.A R P E R RORS- AT . EVEN 

INCREMENTS OF PRESSURE 


RUN NO* HE-0-12 


PRESSURE, ATM. 

Z 

SZ 

1.000E-00 

I.OOO5265795£-00 

7.51851E-07 

2.000E-00 

1.00I0530659E—00 

1.45579E-06 

5.000E-00 

1*0026319658E-00 

3.48087E-06 

1.OOOESOl 

1*00526160I6E~00 

6.72015E-06 

2 • 500ES0I 

I*0131365298£-00 

1•59834E-05 

5.OOOESOI 

1.0262148117£-00 

3.06505E-05 

7.5G0ES01 

1.0392348457E”00 

4.47039E-05 

1•OOOES02 

1.0521966317E-00 

5.82696E-05 

1.250EE02 

1*0651001697E—00 

7.13935E-05 

1.500E602 

1.0779454598E-00 

8.40927E-05 

2.000ES02 

1.1034612962E-00 

1.08222E-04 

2.500EC02 

1.1287441408E-00 

1.30611E-04 

3.GOOEEG2 

1.1537939935E-00 

1.51163E-04 

3.50GESG2 

1.1786108545£-00 

1.69762E-04 

4.G0GES02 

1.2031947237E-00 

1.86286E-04 

4.500ES02 

1.2275456011E-00 

2.00612E-04 

5•Q00E&G2 

1.2516634867E-00 

2.12623E-04 

6.OOOESG2 

1.2992002825E-00 

2.29254E-04 

7.G00EEG2 

1.3458051111E-00 

2.35410E-04 

8.0QGECQ2 

1.3914779725E—00 

2.30566E-04 

9.000EE02 

1.4362188667E-00 

2.14624E-04 

1•000EC03 

1.4800277938E-00 

1.88373E-04 



























































































■ 































































93 


TABLE 


7. - COMPRESSIBILITY FACTORS AND STANDARD ERRORS AT EVEN 



INCREMENTS OF PRESSURE 



RUN NO. HE-0-13 


ESSURE, ATM. 

2 

SI 

1•000E-00 

I» 0005382078E—OQ 

3.96618E-06 

2.000E-00 

1.00107 63069E—00 

7.67250E-06 

5.000E-00 

1.GO26899509E—GO 

1.83218E-05 

l.OOGECGl 

1.0053771804E-0G 

3.53373E-05 

2.500EEG1 

1.0134225412E“00 

8.39470E-05 

5.000EC01 

1.0267770490E-00 

1.6G878E-04 

7.50GEEQ1 

1.0400635234E-00 

2.34610E-04 

1•GGGECG2 

1.0532819644E-00 

3.05 829E-04 

1•250EC02 

1.066432372QE-00 

3.74786E-04 

1•500EC02 

1•0795147462E-00 

4.41574E-04 

2.QG0ES02 

1•1054753944E-00 

5.68687E-04 

2.50GES02 

1.1311639090E-00 

6.86931E-04 

3.000EC02 

1.1565802899E-00 

7.95803E-04 

3« 500EC02 

1.1817245372E-00 

8.94700E-04 

4.OOOEC02 

1.2065966509£-GO 

9.82982E-04 

4.5QQE&G2 

1.2311966310E-00 

1.06001E-03 

5.GQ0E&Q2 

1.2555244774E-00 

1.12518E-03 

6.0006C02 

1.3033637695E-00 

1•2176T§“03 

7.000E&02 

1.3501145270E-00 

1.25653E-03 

8.COOE8G2 

1.3957767501E-00 

1.23910E-03 

9.000E&02 

1.4403504386£“00 

1.16478E-03 

1.000EC03 

1*4838355927E-00 

1« 03689£*=03 






















































• 








































• 


















































94 


TABLE 7.- COMPRESS IBIt ITY FACTORS AND STANDARD ERRORS AT EVEN 


.ESSURE, ATH. 

INCREMENTS OF PRESSURE 

RUN NO« HE-0-14 

l 

SZ 

1•OOOE—OO 

I * 0005266204E-00 

8.56544E-07 

2.OGGE-0O 

1•0010531477E—00 

1* 65852E-06 

5•G0QE-00 

1.0026321695E—00 

3.96571E-06 

1» QOOEEOl 

1.0052620069E-00 

7•656286-06 

2*500EE01 

1 <.01313 75 254 E-00 

1*82102E-05 

5•OOOEEQl 

1•02621674466—00 

3.49209E-05 

7.5G0ESQ1 

1•0392376575E—00 

5* 09322E-05 

1* QQQEEQ2 

1*0522002641£—00 

6 * 63874E-05 

1 *25GEEQ2 

1•0651045644E-00 

8.13390E-05 

1 *500EE02 

1.0779505584E-00 

9.58061E-05 

2 * G0QEE02 

1*10346762776—00 

1.23293E-04 

2.500EE02 

1*1287514718E-00 

i•48795E-04 

3•000EE02 

1.1538020908E-00 

1•72201E-04 

3* 500EE02 

l«1786194846E-00 

1 * 93380E-04 

4.000EE02 

I.2032036534E-00 

2*12193E-04 

4.500EE02 

1.2275545970E-00 

2.28499E-04 

5«0OOEEO2 

1*25167231556-00 

2•42162E-04 

6* 000EE02 

1.2992080770E-00 

2* 61063E-04 

7.000EE02 

1.3458109381E-00 

2* 68017E-04 

8.000E802 

1*3914808986E-00 

2 « 62429E-04 

9.000EE02 

1.4362179586E-00 

2.44190E-04 

1•000E&Q3 

1*4800221181E-00 

2.14211E-04 

























. 

■ 




































' 

' 




















* 





































































































95 


TABLE 


7. - COMPRESSIBILITY FACTORS AND STANDARD ERRORS AT EVEN 

INCREMENTS OF PRESSURE 


RUN NO. HE-G-15 


PRESSURE, ATM, 


SZ 


l.OOOE-QG 

1.0005267123E-00 

8.20047E-07 

2.000E-00 

1.0010533313E-00 

1.58742E-06 

5.000E-00 

1.0026326289E-00 

3.79426E-06 

1•OGOEEOl 

1•0052629261£-00 

7.32320E-06 

2.50GES0I 

1.0131398281E-00 

1.74123E-05 

5.GQOEEOl 

1.0262213653E-00 

3.33865E-05 

7.50QEE01 

1.G392446I16E-00 

4.86957E-05 

1.000ES02 

1•G522095669E-00 

6.34789E—05 

1 * 250EE02 

1.0651162313E—00 

7.77873E-05 

1•500EE02 

1.0779646047E-00 

9.16400E-05 

2•00GES02 

1*1034864786£-00 

1.17986E-04 

2.500EE02 

1.1287751887E—GO 

1.42470E-04 

3.OOGEEQ2 

1 * 1538307349E-00 

1.64988E-04 

3.50QE&02 

1.1786531174E-00 

1.85419E-04 

4.00GE&02 

l•2032423360£-00 

2.03629E-04 

4.500E&02 

1.2275983908E-00 

2.19487E-04 

5 * 000EE02 

1.2517212818E-00 

2•32865E-04 

6.00GES02 

1.2992675723E-00 

2.51705E-04 

7.G00EE02 

1.3458812075£-00 

2.59310E-04 

8•0G06E02 

1.3915621874E—00 

2.55095E-04 

9.000EE02 

1.436310512 IE-00 

2•38902E-04 

1.000EEQ3 

1*4801261814E-00 

2.11439E-04 




















































■ 





































































) 



















*V 

















































































96 


TABLE 7. - COMPRESSIBILITY FACTORS AND STANDARD ERRORS AT EVEN 

INCREMENTS OF PRESSURE 


RUN NO. HE-0-16 


PRESSURE, ATM. Z SZ 


1.000E-00 

1« GOG5264033E“GO 

7.44095E-07 

2.000E-00 

I.0010527I39E—GO 

1.44048E-06 

5.000E-00 

1.00263I0890E-00 

3.44334E-06 

1•OOOECOl 

1.0052598585E—00 

6.64633E-06 

2® 500ES01 

1.0131322492E—00 

1.58041E-05 

5.000ES01 

1.0262065083E“00 

3.03040E-05 

7.50GESG1 

1.0392227772E”00 

4.41997E-05 

1•000ESG2 

1.0521810559E~00 

5•7617IE—05 

I.250E&02 

1« 0650813443E—Q0 

7.06024E-05 

1•500E&02 

1.0779236425E—00 

8.31728E-05 

2•000ES02 

1.1034342683£-00 

1.07076E-04 

2.500ECG2 

1.1287129333E-00 

1.292838-04 

3.000EC02 

1.1537596373E-00 

1.497QIE-04 

3.500EC02 

1.1785743806E-00 

1.68217E-04 

4.000EE02 

1.2031571629E—00 

1•8471IE-04 

4.500ESQ2 

1.2275079844E-0G 

1.99063E-04 

5.00QEC02 

1.2516268451E-00 

2.11157E-04 

6•000EC02 

1.299168683800 

2.28138E-04 

7.OOOEEQ2 

1•3457826791E-00 

2.34892E-04 

8.00GESG2 

1•3914688309E-00 

2.30888E-04 

9.000ES02 

1.4362271393E-00 

2.15990E-04 

1•0QGE603 

1.4800576043E—GO 

1.90863E-04 






















> 

















































. 
















• 

. • 











. 

























































97 


TABLE 7. - COMPRESSIBILITY FACTORS AND STANDARD ERRORS AT EVEN 

INCREMENTS OF PRESSURE 


RUN NO. H£-Q”17 


PRESSURE, ATN. 

Z 

SZ 

L.000E-00 

1.0005265754E-00 

7.27752E-G7 

2.G00E-00 

1.0010530577E-00 

1•40912E-06 

5.GG06-00 

1.00263I9452E-00 

3.36929E-06 

1.OOOECG1 

1.0Q52615599E“00 

6.50473E-06 

2.500E801 

1.0131364209E~00 

1•54710E-05 

5•OGOECOI 

1.0262145789E—00 

2.96679E-05 

7.5GGEL01 

1.0392344737£—00 

4.32708E-05 

1•00GECG2 

1.0521961055E“00 

5.64016E-05 

1.250ES02 

1.0650994742E—00 

6.91049E—05 

1 • 500ES02 

1.0779445798E-00 

8.13971E-05 

2.00GEG02 

1.1034600018E-00 

1.Q4753E-04 

2.5G0EC02 

1.1287423714E-Q0 

1.26425E-04 

3.00GECG2 

1.1537916888E—00 

1.46318E—04 

3 *500E&02 

1.1786079539E—00 

1.64322E-04 

4.0G0E802 

1.2031911666E'-00 

1.80318E-04 

4* 50GEC02 

1.2275413271E~00 

1.94187E-04 

5.00GEG02 

1.2516584352E-00 

2o 05813E-04 

6.000ES02 

1•2991934946E—00 

2.21916E-04 

7.00GE602 

1® 3457963448E-00 

2.27880E-04 

8 .000E&02 

1.3914669857E-GO 

2 o 23198E-04 

9.G0GES02 

1.4362054174 E-= 00 

2.07775E-04 

1•000ES03 

1.4800116398E—00 

1.82373E-04 









/ 



































• 









V - ^ t t ' 











































98 


TABLE 7- COMPRESSIBILITY FACTORS AND STANDARD ERRORS AT EVEN 

INCREMENTS OF PRESSURE 


RUN NO. HE-0-18 


PRESSURE, ATM* Z SZ 


1.000E-00 

1 *0QG526341GE-0G 

6*514196-07 

2.000E-00 

1*0010525893E—GO 

1*26110E-06 

5 * GQOE-OO 

1*00263077746“00 

3 * 01467E-06 

I.OOOECOl 

1*0052592351E-GO 

5*81907E-06 

2•5006601 

1*01313069006-00 

1•38374E-05 

5•G00E801 

1 * 0262033871E—00 

2* 65333E-05 

7 *5006601 

1*0392180912£~00 

3 * 86999E-05 

1*0006802 

1*0521748023E-00 

5 * 04473E-05 

1*2506802 

1*06507352056—00 

6.181596-05 

1 *5006802 

1*07791424566-00 

7*282086-05 

2 * 0006802 

I*10342171686“00 

9.37452E-05 

2-500E802 

1*1286972161E—00 

1 *13182E-04 

3.00QE802 

1 *1537407434E—00 

1*310496-04 

3 • 500E802 

1.1785522988E-00 

1*472486-04 

4.00GE8Q2 

1*203131882 IE-00 

1*616746-04 

4.500E802 

1 * 2274794935E—00 

1*742216-04 

5.000E802 

1*2515951329E-00 

1 * 84789E-04 

6 « 0006802 

1*29913049586-00 

1* 99603E—04 

7 * 0G0E802 

1*34573797086-00 

2.05450E-04 

8 *00GE802 

1*3914175579E-00 

2*018666-04 

9 * 00GE802 

1*43616925716-00 

1*887356-04 

1 0 0Q0E803 

1*47999306846-00 

1*666516-04 































































































\ 





■ • 
















■ 












. 






































































X 






























99 


TABLE 7. - COMPRESSIBILITY FACTORS AND STANDARD ERRORS AT EVEM 

INCREMENTS OF PRESSURE 


RUN NO * HE-0-19 


PRESSURE, 


ATM. 


Z 


SZ 


l.QOOE-OG 
2.00GE-00 
5.000E-00 
1•OOOECOl 
2 • 500EC01 
5.OOOEEOl 
7.500EC01 
1.G00EC02 
1.250EE02 
1.500EE02 
2.000EC02 
2•500EC02 
3.000EC02 
3.500EEQ2 
4•000EC02 
4.500E&02 
5.000EE02 
6.OQOEC02 
7.000EE02 
8•0G0EC02 
9.0Q0EC02 
1•000EC03 


1.Q005267632E-G0 
1.0010534330E-00 
1.0026328813E=00 
1.0052634250E = 00 
1.0131410297E-00 
1o0262236167E—00 
1.0392477610E-00 
1.0522134625E“Q0 
1.0651207213E-00 
1.0779695373E-00 
1.1034918412£-00 
1.1287803742E~00 
1.1538351362£—00 
1.1786561272E-00 
1.2032433473E-00 
1.2275967964E-00 
1.25171647 46 E-=00 
1.299254518IE-00 
1.3458574778E-00 
1. 3915253537E-00 
1.4362581457E-00 
1.4800558540E“00 


8.31151E-07 
1.60948E-06 
3.84884E-06 
7.43125E-06 
1.76765E-05 
3.38987E-05 
4.94407E-05 
6.4441IE-05 
7.89505E-05 
9.29874E—05 
1.19648E-04 
1.44371E-04 
1.67048E-04 
1.87549E-04 
2.05740E-04 
2.21482E-04 
2.34646E-04 
2.52749E-04 
2.59196E-04 
2 . 53414E-04 
2<> 35319E-04 
2 o 0585GE-Q4 



























































■ 
























' 


■ - 














































100 


TABLE 7. - COMPRESSIBILITY FACTORS AND STANDARD ERRORS AT *EVEN 

INCREMENTS OF PRESSURE 


RUN NO. HE-0-20 


PRESSURE 9 


ATM 


Z 


SZ 


1.0Q0E-00 
2 o 0OOE-OO 
5.0G0E-00 
1.000EC01 
2.50GEE01 
5•OOOESO1 
7 o 500EE01 
1.0Q0EE02 
1.250ES02 
1.500EC02 
2•000EE02 
2•500EE02 
3.000EC02 
3.500EC02 
4.000EE02 
4.500EE02 
5.000EC02 
6.000EE02 
7•OOOE&Q2 
8* Q00EE02 
9* 000EC02 
1.000EE03 


1 © 0005268678E”00 
1.0010536418 E-* 00 
1.0026334010E”00 
1«0052644573E~00 
1.0131435574E-00 
1.0262284946£—00 
1.0392 548118£—00 
1.0522225088 E*= 00 
1.0651315857E-00 
1®0779820424E”00 
lo1035070956E“00 
1.1287976682E—00 
1.1538537603E-00 
1.1786753720E-00 
lc2032625030E~00 
1.2276151536E-00 
1.2517333237E-00 
1.2992662223E-0Q 
1« 3458611989E-0Q 
1.3915182534E-00 
lo 43 6237385 9£”*00 
1.4800185963E-00 


7,387G9E~07 
1. 43090E-06 
3.42318E—06 
6.61141E-06 
lo 57318E-05 
3cQ1732E-05 
4.40Q52E-05 
5.73493E-05 
7.02493E-05 
8«27209E-05 
lo06381E-04 
1* 28279E-04 
1o 48316E“04 
1. 66375E-04 
1« 82332E-04 
1o 96Q64E-04 
2.07453E-04 
2.22765E-04 
2 o 27510E-04 
2 o 21198E-04 
2 o 0382 IE-04 
1o 76417E-04 


























. 

■ 





























































































































101 


TABLE 7. - COMPRESSIBILITY FACTORS AND STANDARD ERRORS AT EVEN 

INCREMENTS OF PRESSURE 


RUN NO*. HE—0—21 


PRESSURE ? ATM*. 

l 

SZ 

1 *> OOOE—00 

1 * 0005256146E—00 

7 * 59786E-07 

2.000E-0G 

lo0010511385E—00 

lo46788£-06 

5.000E-00 

1o 0026271653E-00 

3*49908E-06 

1.000E801 

1*0052520604E—00 

6o 73967E-06 

2 *. 5OOE&01 

lo0131131250E“00 

1« 59863E-05 

5 ® 0Q0EC01 

1 * 0261694964E-00 

3o 06198E-05 

7« 500E801 

1*. 039169114 IE—00 

4 * 46642E-05 

1 * 0Q0E&02 

1<.0521119781E“00 

5o 82598E-05 

1*> 25GE802 

1 * 0649980885E—OQ 

7*. 14606E-05 

1.500E802 

1« 0778274452E-00 

8o 42892E—05 

2•Q0QE802 

1 *.1033158975 E—00 

1o Q8851E-04 

2* 500EC02 

1« 128577335 IE—00 

1o 31926E-04 

3o000EC02 

1 *.1536117581E-00 

1o 53440E-04 

3 * 500EE02 

1*. 1784191663 E—OQ 

1o 73296E-04 

4* 000E802 

1*2029995598E-00 

1o 91385E-04 

4«» 500EC02 

1*2273529386E-00 

2o 07598E-04 

5•000E802 

1*.2514793028E~00 

2*. 21829E-04 

6 .000E&02 

I*2990509869E-00 

2o43927E-04 

7 ®000E&02 

1 *> 34 57146122 E-00 

2 « 569286-04 

8.Q00EC02 

1 o 3 914701787 E*" 00 

2o 60230E-Q4 

9.000E802 

1 o4363176864E~0Q 

2-53461E-04 

U0GGE803 

1o 4802571353E-00 

2o 36629E-04 



















































. 



























































. 












































102 


TABLE 7.- COMPRESSIBILITY FACTORS AND STANDARD ERRORS AT EVEN 



INCREMENTS OF PRESSURE 



RUN NO* HE-0-22 


PRESSURE, ATM. 

Z 

SZ 

1.000E-00 

1 o 0005281723E“00 

5.95831E-G7 

2•000E-00 

1 o GO10562473E—00 

1*15804E-06 

5 * OOQE-OQ 

1* 0026398888E“00 

2.78308E-06 

1*OOOESOl 

1*0052773456E-00 

5 * 39314E--Q6 

2 * 50GEE01 

1*0131751242E = 00 

1* 28792E-05 

5 -OOOECO1 

1 * 0262894485£“00 

2* 47253E-05 

7» 500EE01 

lo0393429728£~00 

3.60221E-05 

1.G00E802 

1*0523356973E—00 

4* 6851IE-05 

1.250E802 

lo0652676218E“00 

5* 72382E—05 

1.500E602 

1*0781387465E~00 

6.71889E-05 

2* 00GES02 

1*1036985960E~00 

8 » 57608E—05 

2* 500E8G2 

1*1290152458E~00 

1* 02487E-04 

3 *000E&02 

1 *1540886959E-0G 

1*17259E-04 

3 * 5QGE802 

1 * 1789189464E-00 

1.29954E-04 

4*00QEC02 

1 « 2035059972E“00 

lo40452£-04 

4. 5QQEEG2 

1o2278498484E“0Q 

1o 48636E-04 

5* Q00EE02 

1 * 2519504999E“00 

1« 54399E-04 

6 » 000EC02 

1*2994222038E~00 

1 * 58300E—04 

7 * 0Q0EE02 

1 © 3459211091E“00 

1 * 5 1656E-04 

8 .000EE02 

1*3914472156E“00 

1 * 34617E-04 

9.000EE02 

1*4360005235E-00 

1 * 09142E—04 

1 o 000EGO3 

lo 47958 10327 £*=■ 00 

8 * 38019E-05 


















































































































I 






, 2 D *S 








* 




















■ 


























































103 


TABLE 

Run No. 

HE-0-1 
HE-0-2 
HE-0-3 
HE-0-4 
HE-0-5 
HE-0-6 
HE-0-7 
HE-0-8 
HE-0-9 
HE-0-10 
HE-0-11 
HE-0-12 
J./HE-0-13 
HE-0-14 
HE-0-15 
HE-0-16 
HE-0-17 
HE-0-18 
HE-0-19 
HE-0-20 
HE-0-21 
HE-0-22 

Average 

Average 

Standard 


8. - Compressibility apparatus zero pressure volume ratio 

N Deviation from Average N 


1.994538+0.000103 

-0.000121 

1.994597+0.000117 

-0.000062 

1.994559+0.000130 

-0.000100 

1.994589+0.000118 

-0.000070 

1.994646+0.000129 

-0.000013 

1.994577+0.000102 

-0.000082 

1.994655+0.000101 

-0.000004 

1.994645+0.000122 

-0.000014 

1.994683+0.000054 

+0.000024 

1.994710+0.000101 

+0.000051 

1.994686+0.000110 

+0.000027 

1.994680+0.000092 

+0.000021 

1.993266+0.000489 

-0.001393 

i.994671+0.000105 

+0.000012 

1.994689+0.000101 

+0.000030 

1.994711+0.000092 

+0.000052 

1.994707+0.000089 

+0.000048 

1.994727+0.000080 

+0.000068 

1.994710+0.000102 

+0.000051 

1.994698+0.000090 

+0.000039 

1.994776+0.000100 

+0.000117 

1.994590+0.000064 

-0.000069 


N = 1.994659+0.000022 


standard error of N = +0.000100 
error of a single N = +0.000062 


1 / 


The value of N for this run was omitted from the calculations. 
















































. . ' - 




























/ 
























• 
















, ■ 





■ 








































































































104 

average N, the average standard error of N, and the standard error 
of a single N. 

Values for the constant B of equation (10) at 0° C for each of 
the twenty-two runs are recorded in table 9 along with the average 

B, the standard error in the average B, the average standard error 
of B, and the standard error of a single B. 

Values for the constant C of equation (10) at 0° C for each of 

the twenty-two runs are recorded in table 10 along with the average 

C, the standard error in the average C, the average standard error 
of C, and the standard error of a single C. 

Values for the compressibility factor of helium at 0° C and 1 

atmosphere for each of the twenty-two runs are recorded in table 11 

along with the average Z, the standard error in the average Z, the 
average standard error of Z, and the standard error of a single Z. 

Values for the compressibility factor of helium at 0° C and 
700 atmospheres for each of the twenty-two runs are recorded in 
table 12 along with the average Z, the standard error in the average 
Z, the average standard error of Z, and the standard error of a 
single Z. 

The data for run No. HE-0-13 are not consistent with the data 
of the other twenty-one runs. No error was found in the calculations 
of run No. HE-0-13; therefore, an error must have been made in the 
experimental observations for that run. The data for run No. HE-0-13 
were omitted from the calculations of the various average quantities 
and standard errors of tables 8, 9, 10, 11, and 12. 



' 

* 

■ 










105 


TABLE 9. - Values for the constant B at 0° C 


Run No. 

4 -1 

B x 10 , atm 


' — T _ 

x lO 4- , atm 

HE-0-1 

5.27866+0.00751 


+0.00989 

HE-0-2 

5.27098+0.00808 


+0.00221 

HE-0-3 

5.27706+0.00884 


+0.00829 

HE-0-4 

5.27169+0.00795 


+0.00292 

HE-0-5 

5.26881+0.00878 


+0.00004 

HE-0-6 

5.27408+0.00694 


+0.00531 

HE-0-7 

5.26728+0.00685 


-0.00149 

HE-0-8 

5.26555+0.00831 


-0.00322 

HE-0-9 

5.26935+0.00375 


+0.00058 

HE-0-10 

5.26378+0.00679 


-0.00499 

HE-0-11 

5.26581+0.00744 


-0.00296 

HE-0-12 

5.26626+0.00629 


-0.00251 

1/HE-0-13 

5.38262+0.03298 


+0.11385 

HE-0-14 

5.26667+0.00717 


-0.00210 

HE-0-15 

5.26759+0.00685 


-0.00118 

HE-0-16 

5.26450+0.00622 


-0.00427 

HE-0-17 

5.26622+0.00609 


-0.00255 

HE-0-18 

5.26387+0.00544 


-0.00490 

HE-0-19 

5.26810+0.00696 


-0.00067 

HE-0-20 

5.26915+0.00620 


+0.00038 

HE-0-21 

5.25660+0.00624 


-0.01217 

HE-0-22 

5.28221+0.00514 


+0.01344 

Average 

B = 5.26877 x 10~ 4 + 0.00149 x 10" 4 

atm 


Average 

standard error of B = +0.00685 x 10 

-4 „ -1 

atm 


Standard error of a single B = + 0.00568 x 

-4 

10 atm 

1 

1/ The 

value of B for this run was omitted 

from the 

calculations. 


































































































































































































































106 


TABLE 10. - Values for the constant C at 0° C 


(Deviation from Average 


Run No. 

r 

C x 10 , atm 


x 10 , atm 

HE-0-1 

-4.7891+0.0552 


-0.1102 

HE-0-2 

-4.6933+0.0554 


-0.0144 

HE-0-3 

-4.7391+0.0596 


-0.0602 

HE-0-4 

-4.6812+0.0533 


-0.0023 

HE-0-5 

-4.6667+0.0596 


+0.0122 

HE-0-6 

-4.7037+0.0467 


-0.0248 

HE-0-7 

-4.6647+0.0461 


+0.0142 

HE-0-8 

-4.6425+0.0561 


+0.0364 

HE-0-9 

-4.6921+0.0260 


-0.0132 

HE-0-10 

-4.6348+0.0454 


+0.0441 

HE-0-11 

-4.6522+0.0500 


+0.0267 

HE-0-12 

-4.6598+0.0426 


+0.0191 

J./HE-0-13 

-5.4427+0.2190 


-0.7638 

' HE-0-14 

-4.6645+0.0486 


+0.0144 

HE-0-15 

-4.6633+0.0458 


+0.0156 

HE-0-16 

-4.6392+0.0416 


+0.0397 

HE-0-17 

-4.6610+0.0412 


+0.0179 

HE-0-18 

-4.6394+0.0365 


+0.0395 

HE-0-19 

-4.6754+0.0473 


+0.0035 

HE-0-20 

-4.6896+0.0428 


-0.0107 

HE-0-21 

-4.5403+0.0378 


+0.1386 

HE-0-22 

-4.8640+0.0423 


-0.1851 

Average 

C = -4.6789 x 10~ 8 + 0.0137 x 10" 

' 8 atm" 2 


Average 

standard error of G = + 0.0467 x 

10“ 8 atm" 2 



-8 

Standard error of a single C = + 0.0628 x 10 atm 


1/ The value of C for this run was omitted from the calculations. 


C) 







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107 


TABLE 11. - Compressibility factor for helium at 0° C and 1 atmosphere 


Run No. 

Compressibility factor, Z 

Deviation from Average Z 

HE-0-1 

1.000527818+0.000000886 

+0.000000988 

HE-0-2 

1.000527051+0.000000964 

+0.000000221 

HE-0-3 

1.000527659+0.000001058 

+0.000000829 

HE-0-4 

1.000527122+0.000000952 

+0.000000292 

HE-0-5 

1.000526834+0.000001049 

+0.000000004 

HE-0-6 

1.000527361+0.000000830 

+0.000000531 

HE-0-7 

1.000526681+0.000000819 

-0.000000149 

HE - 0 - 8 

1.000526508+0.000000993 

-0.000000322 

HE-0-9 

1.000526888+0.000000447 

+0.000000058 

HE-0-10 

1.000526331+0.000000813 

-0.000000499 

HE-0-11 

1.000526534+0.000000890 

-0.000000296 

HE - 0 -12 

1.000526580+0.000000752 

-0.000000250 

l/HE-0-13 

1.000538208+0.000003966 

+0.000011378 

* HE-0-14 

1.000526620+0.000000857 

-0.000000210 

HE-0-15 

1.000526712+0.000000820 

-0.000000118 

HE-0-16 

1.000526403+0.000000744 

-0.000000427 

HE-0-17 

1.000526575+0.000000728 

-0.000000255 

HE-0-18 

1.000526341+0.000000651 

-0.000000489 

HE-0-19 

1.000526763+0.000000831 

-0.000000067 

HE-0-20 

1.000526868+0.000000739 

+0.000000038 

HE-0-21 

1.000525615+0.000000760 

-0.000001215 

HE-0-22 

1.000528172+0.000000596 

+0.000001342 


Average Z * 1.000526830 + 0.000000179 
Average standard error of Z * +0.000000818 
Standard error of a single Z ■ +0.000000567 


1 / 


The value of Z for this run was omitted from the calculations. 






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108 


TABLE 12. - Compressibility factor for helium at 0° C and 700 

atmospheres 


Run No. 

Compressibility factor, Z 

Deviation from Average Z 

HE-0-1 

1.346040+0.000257 

+0.000152 

HE-0-2 

1.345972+0.000298 

+0.000084 

HE-0-3 

1.346173+0.000332 

+0.000285 

HE-0-4 

1.346080+0.000300 

+0.000192 

HE-0-5 

1.345950+0.000328 

+0.000062 

HE-0-6 

1.346138+0.000261 

+0.000250 

HE-0-7 

1.345853+0.000257 

-0.000035 

HE-0-8 

1.345840+0.000312 

-0.000048 

HE-0-9 

1.345863+0.000137 

-0.000025 

HE-0-10 

1.345754+0.000257 

-0.000134 

HE-0-11 

1.345810+0.000280 

-0,000078 

HE-0-12 

1.345805+0 000235 

-0.000083 

l/HE-0-13 

1.350115+0.001257 

+0.004227 

HE-0-14 

1.345811+0.000268 

-0.000077 

HE-0-15 

1.345881+0.000259 

-0.000007 

HE-0-16 

1.345783+0.000235 

-0.000105 

HE-0-17 

1.345796+0.000228 

-0.000092 

HE-0-18 

1.345738+0,000205 

-0.000150 

HE-0-19 

1.345857+0.000259 

-0.000031 

HE-0-20 

1.345861+0.000228 

-0,000027 

HE-0-21 

1.345715+0 000257 

-0.000173 

HE-0-22 

1.345921+0.000152 

+0,000033 


Average Z * 1.345888 + 0.000056 
Average standard error of Z = + 0.000255 
Standard error of a single Z * + 0.000129 


1 / 


The value of Z for this run was omitted from the calculations. 













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109 


DISCUSSION OF RESULTS 

Examination of table 5 reveals that the signs of the differ¬ 
ences between the observed and calculated pressures for the various 
runs are not random. This suggests that the assumed functional 
form does not adequately represent the data. 

The influence of changes in the distortion coefficients and 

O' , the effect of adding another constant (D) to equation (10), 
i+Z 

and the effect of changing the coefficient b of equation (4) will 
be explored in a future report. 

A comparison of the data of this report with the data of other 
investigators, and statements concerning the precision and accuracy 
of the data of this investigation will be deferred until the above- 
mentioned tests are completed. 








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110 


REFERENCES 

(_1) Barieau, R. E. The Density of Moist Air from 0° to near 25° C 
and Near Atmospheric Pressure. Helium Research Center Internal 
Report 36, August 1963, 20 pp. 

(2} Briggs, T. C. Temperature Measurement with Leeds and Northrup 
Platinum Resistance Thermometer No. 1586182, Helium Research 
Center Internal Report 53, June 1964, 17 pp. 

(73) _. Measurement of Atmospheric Pressure with Fortin Baro¬ 

meter, Serial No. 13346. Helium Research Center Internal Report 
68, January 1965, 39 pp. 

(4) _. Experimental Determination of a Distortion Coefficient 

at 30° C. Helium Research Center Memorandum Report 67, May 
1965, 10 pp. 

(I) . Elastic Distortion of the High Pressure Compressibility 
Bombs at 30° C. Helium Research Center Internal Report 77, June 
1965, 23 pp. 

(6) __Elastic Distortion of the High Pressure Compressibility 

Bombs at 0° C. Helium Research Center Memorandum Report 71, 

July 1965, 13 pp. 

(J) _Elastic Distortion of the High-Pressure Compressibility 

Bombs over the Temperature Range 0° to 80° C. Helium Research 
Center Internal Report 84, February 1966, 39 pp. 

(8) Brombacher, W. G., D. P. Johnson, and J. L. Cross. Mercury 

Barometers and Manometers. National Bureau of Standards Mono¬ 
graph 8, May 20, 1960, 59 pp. 






















■ 












■ 


























Ill 




r 


(9) Burnett, E. S. Compressibility Determinations Without Volume 

Measurements. J. Appl. Mech., Trans. ASME 58, 1936, pp. A-136- 
A-140. 

(10) Cross, J. L. Reduction of Data for Piston Gage Pressure Measure¬ 
ments. National Bureau of Standards Monograph 65, June 17, 1963, 
9 PP* 

(11) Dalton, B. J. Local Value of Acceleration of Gravity at the 
Helium Research Center (Potsdam System). Helium Research Center 
Memorandum Report 43, April 1964, .13 pp. 

(12 ) Dalton, B. J., and R. E. Barieau. Derivation of Formulas for 

Evaluating the Standard Errors in B, C, and ^p_Q Which Appear in 

the Equation: Z = (Z /P)f n P . Helium Research Center 
^ r o o P=0 r 

Internal Report 69 (Rev.), October 1965, 38 pp. 

(13 ) Osborne, N. S., H. F. Stimson, and D, C. Ginnings. Thermal 
Properties of Saturated Water and Steam. J. Res. Nat. Bureau of 
Standards, v. 23, August 1939, p. 263. 

















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