846 



SCIENCE. 



[N. S. Vol. IX. No. 233. 



its essence consists not in any value it may as- 

 sume, but in our power over it to make it small 

 at will. The advantage of introducing the in- 

 finite in connection with the infinitesimal is not 

 availed of; the former notion is, in fact, not de- 

 fined at all. Similarly, the discussion of infini- 

 tesimals of higher order would have been en- 

 hanced by mention at least of the complementary 

 topic. The author retains the entire respect- 

 able but obsolescent definition of algebraic 

 function, the modern definition of such function 

 as the root of an equation having coefficients 

 rational in the independent variable, being ap- 

 parently nowhere employed. Continuity is not 

 adequately treated, and this preeminently im- 

 portant subject will doubtless be accorded suit- 

 able recognition in the nest volume. Numerous 

 examples of discontinuity, such as are given by 

 Kiepert, are well-nigh indispensable aids to the 

 student, whose attention, moreover, might with 

 profit have been explicithj directed to the fact 

 that the derivability of a function always im- 

 plies, though is not implicit in, its continuity. 

 The idea of uniform continuity is introduced, 

 but only on occasion, as in the deduction of the 

 theorem of total differential. On p. 11 the 



dy 

 dx ' 



tion, and on p. 79, where the differential nota- 

 tion is explained, he is cautioned against ' at- 

 tempting a magnitudinal interpretation ' of du 

 and dx in the 'symbolic equation (h( = i/jidc,' 

 which ' means that the derivative of u as to a; 

 is Wj . ' The author's view of this critical matter, 

 while not in full accord with that, for example, 

 of Jordan's Cows, p. 61, is nevertheless intelli- 

 gible, consistent and adequate. 



The early introduction (Chapter II.) of the 

 notions of integral and integration is attended 

 with obvious advantages. The treatment is good 

 scientifically and pedagogically. A specially 

 commendable didactic feature is the calculation 

 of several integrals by actually making the re- 

 quired subdivisions, forming the corresponding 

 products, generalizing, and throwing the sum- 

 mation into a form suitable for perceiving its 

 limit. 



Space is wanting for briefest comment on 

 many interesting sections as those dealing with 

 illusory forms, maxima and minima, geomet- 



ric interpretation of higher derivatives, change 

 of variable, partial integration, Jacobians, mul- 

 tiple integrals, parametric derivation, and so on. 



It remains to say that not the least praise- 

 worthy quality of the book is found in its style. 

 To be scientific it is not necessary to be vulgar. 

 The volume affords another illustration of the 

 compatibility of rigor and austerity of thought 

 with a generous regard for the amenities of ex- 

 pression. To many the book will be distinctly 

 the more attractive because of its human flavor, 

 its dialectic color, its life, an occasional glance 

 at the philosophic phases of the subject. A 

 rare union of conciseness with precision and 

 clearness is characteristic. For judicious ac- 

 centuation little more could be desired. The 

 reader is taken into confidence, invited to ac- 

 company rather than to follow. The work is 

 not a compilation and not a mechanical struc- 

 ture ; it is rather an organism, a growth, nota- 

 ble for its merits, though, of course, sharing in a 

 measure the imperfections of its kind. 



C. J. Keyser. 



Columbia University. 



Defective Eyesight ; The Principles of its Belief by 

 Glasses. By D. B. St. John Roosa, M.D., 

 LL.D., Professor Emeritus of Diseases of 

 the Eye, New York Post-Graduate Medical 

 School and Hospital ; Surgeon to the Man- 

 hattan Eye and Ear Hospital ; Consulting 

 Surgeon'to the Brooklyn Eye and Ear Hos- 

 pital, etc. New York, The Macmillan Com- 

 pany. 1899. 8vo. Pp. 193. 

 This work is practically a revised edition of 

 the author's little book 'On the Determination 

 of the Necessity for Wearing Glasses,' pub- 

 lished as one of the ' Physician's Leisure Library 

 Series ' in 1887, by George S. Davis, of Detroit, 

 Michigan. 



The volume has gained much by its revision, 

 has had some excellent illustrated matter intro- 

 duced and has been considerably enlarged. 



The subject is divided into seven parts, all of 

 which are written in the author's well-known 

 easy style, making those who have had the 

 pleasure of personally reading his writings 

 more firmly convinced of his earnestness and 

 erudition. 



Considering the subject-matter in its given 



