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fact that the work merely claims to be a pastime. The combinatorial character of 
the first two parts is suggestive of the analogous problem of the magic square. 
There one does not expect a completely analytic treatment except under favorable 
restrictions. The third part deals rather with systematic material affected by 
the presence of arbitrary arcs. It becomes a problem of analysis situs combined 
perhaps with certain non-scientific esthetic demands of minor interest. Possibly 
in the more extensive discussion that the author promises the objections here 
raised may be no longer applicable. 

A useful but limited chronological bibliography of works on mathematical 
recreations is given in the appendix. 

The casual reader may be disappointed in finding no explicit statement of 
puzzles to tax his ingenuity and arouse his interest. The "pastimes" are sug- 
gested rather than directly announced. But any one with a little imagination 
and with a healthy taste for numerical and tactical puzzles will find a fruitful 
source of amusement in this book. A far more instructive book might perhaps 
have been developed upon the same basis of original material but no one should 
demand instruction in any book claiming to offer nothing more than new mathe- 
matical pastimes. 

Albert A. Bennett. 

The excellent Revue de I'Enseignement des Sciences, published by Felix Alcan, 
Paris, 1909-1920, has ceased publication. Its place is taken by Bulletin Scien- 
tifique des Professeurs de I'Enseignement du 2e degrS (B.S. 2) which has been 
published twice a month since October, 1921, at Chaussenueil, France; P. 
Martin, director; 12 francs a year. 

Mr. Roger S. Hoar, a member of the Association, has printed privately a 
discussion of the mechanics of a new design of gasoline power shovel. It is in a 
simple form, convenient for students of elementary mechanics. Any number 
of copies gratis are to be had upon application to him, care of Bucyrus Company, 
South Milwaukee, Wis. This suggestion may appeal to some teacher looking 
for "practical" applications. 

Mr. Harry B. Marsh, head of the department of mathematics in the Tech- 
nical High School, and Springfield Junior College, Springfield, Mass., has published a 
pamphlet: Elementary Algebra Outline based upon College Entrance Requirements 
and Examination Papers (New York, Newson and Co., 1922, 48 pages). 

A twenty-nine page printed report to the College Entrance Examination 
Board upon Elementary Algebra, Advanced Algebra, and Plane Trigonometry 
by the Commission on College Entrance Requirements in Mathematics, 431 West 
117th Street, New York City, has recently been distributed. The Commission's 
Report on Plane Geometry and Solid Geometry is being printed separately. 
The report is elaborate and .specific and should come to the attention of all 
interested in the ground covered in sub-freshman work in mathematics. Pro- 
fessor W. F. Osgood, of Harvard University, is chairman of the Commission. 

We have already indicated {1921, 267) the contents of the first edition of 


Suggestions for Students of Mathematics. Mathematics and Life Activities (7 
pages), issued in March, 1921, by the Department of Mathematics of Brown 
University. An extended review appeared in Mathematics Teacher, volume 14, 
pages 349-350. A third revised and enlarged edition was published in October, 
1922. In this edition a new section is devoted to a "Literature List"; that 
is, a list of 23 books, in English, and in the mathematical library of the University, 
" which may be read with profit — though not in every case with complete under- 
standing — by those who are taking, or have credit for, freshman mathematics." 
A limited number of these pamphlets are available for distribution to those 

Two new parts of the Encyklopadie der Mathematischen Wissenschaften have 
been published April 1 and May 15, 1922, respectively. The first part, V-2-5, 
" Elektronentheorie der Metalle " by Rudolf Seeliger, 15+777-878 pages, com- 
pletes volume V-2. The second part, III-1-9, " abgeschlossen 31 Aug. 1916", is 
" Polyeder und Raumeinteilungen " by Ernst Steinmetz, 1-139, special paging 
in italics. It is announced that III-1-8 with register for III-l will appear later. 
There are now 10 complete part volumes of the Encyklopadie, namely: 1-1, 1-2, 
II-l-l, II-1-2, II-2, IV-1, IV-3, IV-4, V-l, and V-2. 

For many years, 1900-1915, an important feature of Bibliotheca Mathematica 
was a section devoted to " Kleine Bemerkungen " on the latest edition of Cantor's 
Vorlesungen ilber Geschichte der Mathematik. In this way a great many correct- 
ions, and much valuable information, were brought together. In Jahresbericht der 
deuischen Maihematiker-Vereinigung, volume 31, 1922, pages 73-77, a section of 
this kind has been started, and will continue so long as the publication of Biblio- 
theca Mathematica is suspended. In this section there are 11 notes, by Ferdinand 
Rudio, on various passages in Cantor's volume 3, pages 549-624. 


Bulletin op the American Mathematical Society, volume 28, January-February, 
1922: "The twenty-eighth summer meeting of the American Mathematical Society" by R. G. D. 
Richardson, 1-15; A letter from the President of the Society, G. A. Bliss, 16; "Report on 
topics in the theory of divergent series" by W. A. Hurwitz, 17-36; "Note on an irregular expan- 
sion problem" by D. Jackson, 37-41; "The B6cher Memorial Prize" by E. B. Van Vleck, 42-44; 
"On Kakeya's minimum area problem" by W. B. Ford, 45-53; "Convergence of sequences of 
linear operations" by T. H. Hildebrandt, 53-58; Review by D. Jackson of C. de la Vallee Poussin, 
Lecons sur V Approximation des Fonctions d'une Variable Reelle (Paris, 1919), 59-61; Reviews by 
D. E. Smith of B. Lefebvre, Notes d'Histoire des Mathematiques (Antiquite et Moyen Age) (Bruxelles, 
1920), of Bibliotheca Chemico-Mathematica (2 volumes, London, 1921), and of W. W. Bryant, 
Kepler (London, 1920), by P. Field of P. Burgatti, Lezioni di Meccanica Rationale (2d edition, 
Bologna, 1919), and of C. Burali-Forti and I. Boggio, Meccanica Rationale (Turin and Genoa, 
1921), by A. R. Crathorne of A. Loewy, Mathematik des Geld- und Zahlungsverkehrs (Leipzig and 
Berlin, i920), by V. Snyder of T. Schmid, Darstellende Geometrie, Vol. II (Berlin and Leipzig, 
1921), by H. B. Phillips of F. Reiche, Die Quantentheorie, ihr Ursprung und ihre Entwicklung 
(Berlin, 1921), and by D.N. Lehmer of L.Poletti, Tavole di Numeri Primi entro IAmite Diversi, e 
Tavole Affini (Milan, 1920), 62-71; Notes, 72-82; New Publications, 83-88— March: "The 
October meeting of the American Mathematical Society" by R. G. D. Richardson, 89-94; "The 
October meeting of the San Francisco Section" by B. A. Bernstein, 94-97; "The simple group of 
order 2520" by G. A. Miller, 98-102; "A theorem of oscillation" by W. E. Milne, 102-104; 
"A two-way infinite series for Lebesgue integrals" by M. B. Porter, 105-108; "Note on Euler's