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CXI. Notices respecting New Books. 



The Cambridge Colloquium, 1916. Part J. By G. F. Evans. 



New Y'ork. 191S. Published by the American Mathematical 



Society. 

 r PHIS volume by Professor Griffith C. Evans of the Rice 

 -*- Institute consists of a course of lectures given before the 

 American Mathematical Society at its Eighth Colloquium, held 

 at Harvard University in. 1916. The lectures dealt with the 

 theory of functionals and their applications, and also with various 

 other topics, including the theory of Integral Equations. The 

 second part of the present volume is to contain the lectures of 

 Professor Oswald Veblen of Princeton University on Analysis 

 Situs, which were delivered at the same Colloquium. 



The present lectures select for discussion the general ideas of 

 Hadamard Stieljes, Borel, andLebesguein the theory of functions. 

 It will be of great value to students to have before them in this 

 book so clear an account of these modern developments. The 

 work of recent writers in particular on the Lebesgue integral and 

 on the very important development known as the Stieljes integral 

 is summarized in excellent fashion. This volume and its com- 

 panion volumes should have an excellent effect in stimulating 

 further researches on topics which seem, indeed, to promise further 

 rapid extension. 



A Treatise on the Integral Calculus : with applications, examples, 



and problems. Vol. II. By Joseph Ebwatids. (Macmillan 



& Co., 1922.) 

 We look on this work as our equivalent of Bertrand's treatises. 

 The subject is developed in the good old-fashioned gentlemanly 

 style, and the reader is not tripped up perpetually by an appeal 

 to Rigour, Convergence, Epsilomology, and other impediments on 

 his road — " cherchant toujours la petite bete dans la demon- 

 stration." 



A summary of Elliptic Eunction theory finds a place, useful 

 as a Manual for the applications encountered everywhere in 

 Physical Science. Mention of these applications as they arise 

 may repel the mere mathematician, but will help a reader to a 

 grasp of general theory, as in the application of Compound 

 Representation to discontinuous fluid motion. 



Historical reference too, the valuable feature of Bertrand's 

 style, will add to the interest, as for instance in Mercator's 

 projection, where it appeared long after Napier's invention that 

 Edward Wright's Table of Meridional Parts, 1599, is in reality a 

 series of logarithmic tangents and claimed as such by Wright in 

 his subsequent name of Nautical Logarithms. 



The author does not see his way to the Continental abbreviation 

 of the hyperbolic function, to ch, sh, th, . . . in analogy with the 

 elliptic function en, sn, dn, tn, . . . 



Numerous diagrams, drawn carefully with accuracy, make a 

 pleasing feature of the work. 



