JaNK 29, 1900.] 



SGIENGE. 



1027 



tables, can only be regarded as approximations 

 to the truth. In arranging the computation of 

 such a series of values it becomes a very prac- 

 tical matter so to select the intervals as to 

 avoid unnecessary labor on the one hand and the 

 possible introduction of inadmissible errors in 

 the interpolated values on the other. We have 

 here the practical rule evolved showing that 

 this may ordinarily be accomplished by choos- 

 ing our intervals such that differences beyond 

 the fifth order may be disregarded. Of course, 

 in the very uncommon case of a rational integral 

 function we may reach absolute accuracy by 

 carrying our computation to the point where 

 the differences vanish. 



The subject of mechanical quadrature is 

 doubtless more familiar to the mathematical as- 

 tronomer than to any other class of readers. 

 Owing to the convenience and facility with 

 which it may often be applied to the evaluation 

 of definite integrals it seems to deserve a more 

 prominent place in works treating of applied 

 mathematics than is commonly the case. Here 

 we find the processes of both single and double 

 integration very fully developed, based in turn 

 on Newton, Stirling and Bessel's formula. 



Every one naturally assigns a somewhat ex- 

 alted position to his own special line of investi- 

 gation. It is, therefore, perhaps not surprising 

 to find, on page 79, what to some may appear 

 to be a somewhat ' dark saying, ' viz : ' ' Inter- 

 polation has undoubtedly done more for mathe- 

 matical science than any other discovery except- 

 ing that of logarithms." Not to mention the 

 Arabic system of notation, why may we not 

 with equal propriety make a like assertion in 

 regard to multiplication ? 



Among the problems solved the following 

 are suggestive : 



To solve any numerical equation whatever 

 involving but one unknown quantity. 



Given a series of numerical functions em- 

 bracing a maximum and minimum value. To 

 find the value of the argument which corre- 

 sponds to the maximum and minimum function. 



An appendix deals with symbolical methods. 

 Fifteen pages are given to tables, principally 

 the coefficients in Newton, Stirling and Bessel's 

 formulae, while two pages devoted to the bib- 

 liography of the subject complete the work. 



Naturally a treatise like this will interest 

 only a limited class of readers, such as workers 

 and students in astronomy and mathematical 

 physics. To all these it can be cordially rec- 

 ommended. 



c. l. doolittlb. 



Flowee Obsebvatoey. 



books eeceived. 



Education in the United States. A Series of Monographs 

 prepared for the United States exhibit at the Paris 

 Exposition, 1900. Edited by Nicholas Murray 

 BUTLEE. Albany, N. Y., J. B. Lyon Company. 

 1900. In two volumes. Pp. sviii-|-977. 



Department of Geology and Natural Resources of Indi- 

 ana. 1899. "W. S. Blatchley. Indianapolis, 

 Wm. B. Bnrford. 1900. Pp. 1078. 



North America. Ralph S. Tare and Frank M. 

 McMdeky. New York and London, The Mac- 

 millan Co. 1900. Pp. xis+469. 75 cts. 



Familiar Fish, ilieir Habits and Capture. EUGENE 

 McCarthy, with an introduction by David Staee 

 Jordan. New York City, D. Appleton & Co. 

 1900. Pp. xi4-216. $1.50. 



A Book of Whales. F. E. Beedaed. New York, G. 

 P. Putnam's Sons ; London, John Murray. 1900. 

 Pp. XV + 320. 



Physiology for the Laboratory. Beetha Millaed 

 Beown. Boston, U. S. A., Ginn & Company. 

 1900. Pp. v+167. 



A Brief History of ilathematics. Kael Fink. Trans- 

 lated by W. W. Beman and D. E. Smith. Chi- 

 cago, Open Court Publishing Co. 1900. Pp. xii 

 + 333. ?1.50. 



Exploitation technique desforets. M. H. Vanutbeegh. 

 Paris, Gauther-Villars. 1900. Pp. 176. 



La garance et Vindigo. George F. Jaubeet. Paris, 

 Gauthier-Villars. 1900. Pp. 166. 



Lehrhuch der Photoehromie. Wilhelm Zenker. New 

 edition edited by B. Schwalbe. Braunschweig, 

 F. Vieweg und Sohn. 1900. Pp. xiii + 157. 



Das soziale und siiiliche Leben erkldrt durch die seelische 

 EntwicUung. J. Maek BALDWIN. Translated 

 from the second English edition by De. R. Ruede- 

 MANN, with preface by Dr. Paul Baeth. Leip- 

 zig, J. A. Barth, 1900. Pp. xv + 466. 



SCIENTIFIC JOURNALS AND ARTICLES. 



The Journal of the Boston Society of Medical 

 Sciences for May is more exclusively technical 

 than usual. Harold C. Ernst and W. H. 



