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Stanley B. Fracker 
University of Illinois 

One of the most difficult problems in zoologic science is the classi- 
fication of round worms. Authors and lecturers, after a carefully 
outlined and definitely arranged discussion of trematodes and ces- 
todes, are compelled to consider nematodes in a somewhat desultory 
and inaccurate fashion. Two reasons for this may be given, the 
greater being the apparent lack of a basis for determining the 
phylogeny of the major groups, a condition with which we are not 
at present concerned. The other obstacle is the difficulty of differenti- 
ating between species and uncertainty as to the value of different kinds 
of taxonomic characters. The multitude of synonyms for many of 
our common insects is a sore point among entomologists, but nemat- 
helminthologists have great difficulty in deciding that any particular 
name should be relegated to the synonymy. 

In the absence of definite structural differences, Dujardin in 1846 
found himself compelled to give a few measurements of the length, 
breadth, tail, etc., of the species which he described. This method 
was further applied by Eberth in Germany and Bastian in England, 
followed by Biitschli and others. Finally, in 1890, N. A. Cobb 
arranged a "nematode formula" which he has applied in all his sub- 
sequent work. This formula shows two kinds of measurements : first, 
the length of the worm in millimeters ; second, the percentage of that 
length which is represented by the distance from the anterior end 
of the worm to (a) the base of the pharynx, (b) the nerve ring, 
(c) the cardiac constriction, (d) the vulva, and (e) the anus; and 
also the width of the body at each of these points. He uses the 
formulae of different species, both in descriptions and in keys for 

Cobb has described something over one hundred species of free- 
living round worms of the family Anguillulidae and has always 
worked out and stated the formula. As there are at present no 
other scientists making a specialty of this family, it would be unfair 
to emphasize the fact that, in the quarter century since the descrip- 
tion of this formula, it has been used only by its originator. There are, 

* Contributions from the Zoological Laboratory of the University of Illinois, 
under the direction of Henry B. Ward, No. 31. 


however, many helminthologists concerned with parasitic Nematoda 
where the obstacles of classification are equally great. Some of these 
have seen the possibilities of such a formula, but a real doubt as to 
its value has prevented them from adopting it. Until the following 
questions are answered, one must feel that energy and time invested 
in descriptions of this nature are not well employed: 

1. Can the formula be applied at all to the majority of para- 
sitic species? 

2. Is the camera-lucida method of measurement sufficiently accur- 
ate for such a purpose ? 

3. Are the relative proportions of the different organs constant 
within a single species? 

Cobb has not discussed these points in his published papers. He 
has applied the formula to very few parasitic species and apparently 
not at all to the difficult ones. He has published no warnings con- 
cerning the undoubted distortions caused by the varying tilt of the 
mirror, or the part of it from which a particular organ is reflected. 
In no case, so far as I am aware, does he give any indication that 
he has measured more than one individual of each species. This 
is especially noticeable in view of the fact that he must have had 
numerous specimens of some forms and that general attention has 
been called to this lack in as prominent a place as the Cambridge 
Natural History. 

At the suggestion of Prof. Henry B. Ward of the University of 
Illinois, the writer recently undertook an investigation of the varia- 
tion in the proportion of the organs. Incidentally, fragmentary 
observations on the other two questions are reported. 

Cobb's measurements were made on camera-lucida drawings of 
cleared worms and this procedure has been modified in only one 
particular. Most of the worms measured by the writer were studied 
merely in formalin, only about one-fourth having been dehydrated 
and cleared in carbol xylol. None were mounted in balsam but all 
were studied under a cover-glass. The greatest care was used to 
avoid errors due to faulty technic, such as would be caused by acci- 
dental differences in the position of the camera-lucida. The effect 
of transfering the specimens from formalin to the clearing agent was 
not determined but is probably slight. The first fourteen worms 
whose measurements are reported in the table were cleared. 

The first species of which drawings were made with a view to 
measurement was the hookworm, Necator americanus Stiles. Unfor- 
tunately, this is bent in two planes, the head being hooked at a right 
angle to the general body curvature. In addition, the males, of which 
most of the available material consisted, have the anus at the tip of 


the body. The body wall is so opaque that locations of internal struc- 
ture are difficult to determine, and the writer was unable to discover 
any method of making the nerve ring visible. For these reasons 
the conclusion was reached that the formula could not be satisfac- 
torily used on these worms and work on the species was abandoned. 

Accurate measurement of larger worms, such as Ascaridae, was 
out of the question, no apparatus adaptable to this use being avail- 
able or on the market. These facts partially answer the first two prob- 
lems involved, it being clear, first, that the Strongylidae, especially the 
hookworms, do not readily lend themselves to classification by this 
means ; second, that the camera-lucida method of measurement now 
in vogue is not applicable to worms exceeding 1 cm. in length. Pos- 
sibly the latter obstacle may still be overcome by the use of special 
apparatus if the formula proves its worth in other points. 

The department of zoology then secured about one hundred speci- 
mens of Oxyurias vermicularis Linn., the pinworm of man. These 
were all from one host, living in a rural locality in Kentucky, and were 
all voided at the same time. It soon became clear that, among the 
parasitic genera, Oxyurias is ideal for such work. The specimens were 
preserved in formalin, and at first the vulva could not be located with 
certainty, but clearing in carbolxylol corrected that difficulty. As a 
consequence, the writer was able to make a rigorous test of practically 
all of Cobb's characters except the position of the nerve ring, which 
could not be determined, owing to the preservative. It may be noted 
in passing that the nerve ring is often difficult to locate, one of Cobb's 
largest papers (1893) omitting that character in the formulae of one- 
third of the species. Cobb gives (1890a) the formula for a young 
individual of 0. vermicularis, but its immature condition invalidates 
any possible comparison with the results given here. 

The purpose of this work was not to examine critically the par- 
ticular points located by Cobb, but to ascertain the extent to which the 
proportions of the worm were constant, and the parts which undergo 
the greatest variation. The results should be of interest, both to 
parasitologists and to systematists, regardless of their relation to this 
particular formula or group. 

The unit of measurement used was 1 per cent, of the length of the 
individual. Measurements were made on this basis from the anterior 
end (1) to the caudal margin of the cephalic swelling; (2) to the 
beginning of the esophageal bulb; (3) to the cardiac constriction; 
(4) to the vulva; (5) to the anus; (6) to the anterior and posterior 
limits of the internal reproductive organs. The width at each of 
these points was also determined. Finally, the total length of the 
worm was calculated. Fifty-two individuals were measured, but 


in most of them one character or another was so indefinite that the 
writer did not feel justified in recording what appeared to be its loca- 
tion. This was especially true of the vulva, invisible in uncleared 

The following table gives the measurements of each worm studied. 
In the first column is the arbitrary number of the specimen. The 
second gives the length of the worm in millimeters. The figures in all 
the other columns indicate the percentage of the length of the worm 
from the cephalic end to that particular point, the columns being num- 
bered as in the last paragraph. Column 6, however, shows only the 
interval occupied by the reproductive organs. "L" indicates length 
and "W" width. Finally, for each of these characters, there is 
recorded (a) the average, (b) the number of specimens on which the 
character was determined, (c) the "standard of variation," (d) the 
maximum and (e) the minimum measurement found, and (r) the 
range. The average is the sum of all the measurements divided by (b). 
The standard of variation was calculated by the well-known formula, 

(a- r\l?^'- ), x being the deviation of a class from the average, and 

/, the number in the class. The range is merely the maximum, (d), 
minus the minimum, (e). 

Attention should be called to the fact that results (a) and (c) were 
calculated from measurements to the second decimal place. In order 
to limit space it was thought desirable to omit the second place in the 
printed record. This will explain any slight discrepancies which might 
confuse, should these results be checked over. The lack of value of the 
second or even the first decimal place is discussed in a later paragraph. 

The average length of the body of this species is 7.39 mm. The 
range is about one-fourth of the maximum length. As the curve is 
normal, the total range in the species is probably not much greater 
than this. 

1. The external cephalic swelling is peculiar to the species studied 
and is a secondary development of no great definiteness or importance. 
The curve of the variation in its length is an irregular one and far 
from the normal type. It will be noted that the range is over two- 
fifths of the maximum, and that the standard of variation is 0.397 per 
cent., or about one-ninth of the maximum. In view of the nature of 
this feature, considerable variation was to be expected. 

2. The esophageal bulb marks a distinct division of the alimentary 
canal and is bounded by two definite constrictions. The esophagus, 
which leads from the mouth to this bulb, is straight or slightly bent, 
in no case being sufficiently curved to draw the bulb out of its position. 
Variation is from 8.3 per cent, to 12.1 per cent., a range of 3.8 per cent. 



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The magnitude of the range and of the standard of variation is 

3. The cardiac constriction is the caudal limit of the esophageal 
bulb, which occupies from 2 to 3 per cent, of the length of the worm. 
The distance of this constriction from the mouth varies from 10.4 to 
14.4 per cent., and the range, 4 per cent., is about two-sevenths of the 
maximum. This range overlaps about one-sixth of all the species Cobb 
has described in the papers at hand. 

4. Only thirteen individuals were studied in which the vulva could 
be located, it being invisible in the opaque formalin material. In the 
cleared specimens, the range in its position was about one-third of the 
maximum distance from the mouth. The standard of variation, 3.37 
per cent., is over four times that of any of the first three structures. 

Fig. 1. — Oxyurias vermicularis Linn. Specimen No. 2; lateral aspect of 
cleared worm. 1-6, the structures and distances measured in this paper; for 
explanation see text, and table opposite. 

5. The anus is usually located in the caudal fourth of the body, its 
position varying from 74.2 to 81.4 per cent., a range of 7.2 per cent. 
The standard of variation is 1.78 per cent., or midway between those 
of the last two structures. Some reliance, therefore, can be placed on 
measurements of the location of the anus. 

6. In the use of the formula, the interval occupied by the repro- 
ductive organs is given in an approximate and general way. Cobb 
usually uses a multiple of 10 per cent, to express this distance. Even 
this approximation, however, appears to be of no value in Oxyurias. 
In some cases these organs reach from a point near the mouth (5.7 per 
cent.) to a point behind the anus (86.9 per cent.), often obscuring the 
latter's position. In other specimens they have shrunken to a small 
size or are undeveloped. The interval occupied varies from 37.5 to 
75.1 per cent., a range of 37.6 per cent. Such a condition makes the 
recording of this interval in the specimens at hand when a species is 
described a waste of labor. 

While measurements of the lengths of different structures vary 
independently of each other, this is not true of the widths at different 
points. For this reason separate discussions of the latter are not 
necessary. In almost all cases the range in widths is approximately 
equal to, or greater than, the width of the most slender worm studied. 
So few specimens were measured at the vulva that the range there is 


not as great as it should be, neither the slimmest nor plumpest worms 
having been measured at this point. Taking the width at the cardiac 
constriction as typical, we find a variation of from 2.4 to 6.3 per cent. 
The latter worm was particularly contracted, however, the normal 
range being from 2.4 to 5.4 per cent., as shown by the curve of 

If structures were correlated with each other, considerable reliance 
could be placed on the body proportions in spite of the individual 
variation. It was hoped that a study of correlation would yield results 
which would assist in the interpretation of the relation between an 
unnamed specimen and a given formula. The attempt to find such 
assistance, however, must be considered a failure. 

Correlation diagrams were made to show the relation of the width 
of the body to the length of the esophagus, the length of the alimentary 
canal to the length of the esophagus, the relation of the position of the 
vulva to that of the anus and to that of the cardiac constriction, etc. 
In no case was there the least indication of correlation, except between 
the length of the esophagus and the position of the cardiac constriction. 
As the esophageal bulb which separates these is small and rather con- 
stant in size, this fact can hardly be called a true correlation. 

Much of the importance of a study of variation in its relation to 
classification depends on the differences between the various species 
with the group concerned. Thus, if all Nematoda had an esophagus 
about one-eighth the length of the body, had the vulva placed within 
the cephalic third, and the anus near the beginning of the caudal fourth 
of the total length, a variation no greater than occurs in Oxyurias 
would make the measurement method valueless in identification. The 
formulae of about one hundred species described by N. A. Cobb were, 
therefore, examined in order to determine the variation within the 
class. In some cases curves were plotted. 

This examination showed an ideal condition for such a scheme. 
A curve including the formulae of the described species is similar to 
a long, low mountain range. All possible changes in the proportions 
seem to have been observed. As a result, the range of each of the 
characters given above covers only one-fifth to one-tenth of the 
described species. In some cases it is less than that. For example, 
the vulva, in the eighty-five species whose descriptions happen to be 
before me at the moment, varies from 20 to about 80 per cent, in posi- 
tion. Of these, only five species are between the maximum and mini- 
mum found in the specimens of Oxyurias reported in this paper. 
Forty of them, however, or nearly half, are between 45 and 55 per 
cent., a range less than that in this species. The fact, therefore, that 
the range appears unimportant in this case seems to be an accident of 
the species chosen. 


In tables for identification, Cobb has used such characters as "Tail 
15 per cent.," as opposed to "Tail 20 per cent."; or "Body slender 
(little more than 2.6 per cent.)" in opposition to "Body not so slender 
(3 per cent, or over)." In these and many other places the difference 
specified is less than the range in this one species. 

In general, the variations recorded here may be due to two causes : 
(a) varying state of contraction owing to chemical technic, conditions 
of killing, etc., and (b) ordinary fluctuating variations. General body 
contraction would not affect the positions of the organs and can 
scarcely account for differences in length percentages. On the other 
hand it would have an important effect on the width. Thus the length 
percentages, depending largely on fluctuating individual variations, are 
not correlated with the widths, most of which are determined by the 
state of contraction. The impossibility of securing uniform con- 
traction makes it necessary to consider width measurements unreliable. 

In the practice of identification of specimens two advantages may 
be claimed for a formula. In the first place it is an abbreviated record 
of what would be a long description. This advantage cannot be gain- 
said and is the principal source of the strength of the "nematode for- 
mula." In the second place a comparison of the formula of a speci- 
men at hand with those of a series of descriptions might aid in identi- 
fication. This is the advantage which has been emphasized too much. 
The following are the formulae of a few of the specimens of Oxyurias 
vermicularis : 

No. 1. 7.05 mm. 

No. 2. 7.37 mm. 














31.4 02 




















? 3 ' 












No. 7. 6.87 mm. 

No. 26. 7.46 mm. 

No. 42. 8.05 mm. 

2.0 2.9 3.2 ? 2.4 

These figures do not refer to the exact points used by Cobb, but 
the principle is the same. If the species had been described from No. 7 
and that formula given as typical, it is doubtful whether it would aid 
in naming No. 26 or any of the others. 



The proportionate size of the organs in Nematoda is an important 
factor in their identification and should be stated in any description of 
a new species. 

The locations of the cephalic parts of the alimentary canal tend to 
vary from 1 to 4 per cent., about one-third of the maximum, in Oxy- 
urias vermicularis. 

The location of the vulva probably varies at least 15 per cent, in a 
long series of individuals. 

The location of the anus varies over 7 per cent., or about one-third 
of the length of the tail. 

Variations in width are so great that some individuals are over 
twice as wide as others. 

The length of the body of some individuals is one-third greater 
than that of others. 

The use of the formula is likely to yield more confusion than assist- 
ance. It is impossible to indicate the observed range, and without that 
the numbers are meaningless. Carrying the measurement to one-tenth 
of 1 per cent., gives an appearance of accuracy which does not exist. 
The formula is likely to result in the multiplication of so-called species 
without a proper basis for their separation. 

A species should not be described as new on account of a deviation 
from the proportions of known species unless that deviation is great 
and fundamental. The space occupied by the reproductive organs 
should not be considered, and little dependence should be placed on the 
width of the body. From four to ten individuals should always be 
studied and the observed range recorded. In this way the varying 
proportions of the different species can be used in the identification of 
collected specimens. An individual should never be identified, how- 
ever, on the basis of the formula alone or of the proportions alone. 


Cobb, N. A. 1890. A Nematode Fermula. Agr. Gaz., N. S. W., 11:131-135. 
1890a. Oxyuris Larvae Hatched in the Human Stomach under 

Normal Conditions.. Proc. Linn. Soc, N. S. W., 5 : 

1890b. Arabian Nematodes. Proc. Linn. Soc, N. S. W., 5 : 

1893. Nematodes, Mostly Australian and Fijian. Dept. Agr., 

N. S. W., Misc. Publ. 13, 59 pp. 
1902. The Nematode Fermula. Agr. Gaz., N. S. W., 13:1023- 

1913. New Nematode Genera Found Inhabiting Fresh Water 

and Non-Brackish Soils. Jour. Wash. Ac. Sci., 3:432-