396 



jVA TURE 



[August 22, 1901 



THE CIRCULATION OF THE ATMOSPHERE. 



Mhitoires originaux sur la Circulation gcn^ralc de 

 r Atmosphere. Annotes et Commentes par Marcel 

 Brillouin, Maitre de Conferences a I'Ecole Normale 

 Supi^rieure. Pp. xx+163. (Paris: Georges Carre et 

 C. Naud, 1900.) 



THIS may be described as a French Student's note- 

 book of foreign memoirs upon the general circula- 

 tion of the atmosphere. It contains papers upon the 

 subject, partly translated in full, partly in extract or 

 analysis, by Halley, Hadley, Maury, Ferrel, James 

 Thomson, W. von Siemens, MoUer, C)berbeck and von 

 Helmholtz, with a short introduction and some critical 

 notes to the current text. 



The book may be welcomed as calling attention to a 

 subject which greatly needs attention in this country. 

 But little has been done for it since James Thomson, in 

 the Bakerian lecture of 1892, revived the ideas he had 

 originally put forward at the meeting of the British 

 Association at Dublin in 1857. In the United States 

 Prof. Cleveland Abbe has collected and translated the 

 principal memoirs, but the mathematical treatment of 

 atmospheric circulation has been neglected in England- 

 Contrary to the general experience of scientific books 

 in French, the work is rather dull. The introduction 

 makes it clear that only foreign memoirs are included, 

 and the work of MM. Tastes and Duclaux, as well as 

 that of M. Teisserenc de Bort and of M. Brillouin himself, 

 particularly " \'ents contigus et nuages " [Ann. du Bur. 

 Ccntr. Met. 1898) is only incidentally referred to, but this 

 does not altogether account for the impression. The 

 subject itself is difficult ; indeed, in its details it is far 

 beyond the power of mathematics. No one can suppose 

 that it is possible to deduce the actual motion of the air 

 at this instant at every ])art of the globe from its primary 

 causes, namely the insolation of one half the globe, the 

 radiation from the other half, the force of gravity and the 

 rotation of the earth ; and yet that is what, in a general- 

 ised manner, most of the authors quoted set out to do. 

 Of course, a conventional atmosphere has to be used 

 and a conventional circulation therein accounted for ; 

 and, as a matter of fact, the assumptions and conven- 

 tions that a writer makes in order to bring his powers of 

 calculation to bear are more interesting than the details 

 of elaborate mathematics on artificial hypotheses leading 

 to results which, to put the matter bluntly, are only true 

 in so far as they are not new. 



Von Siemens' application of the principles of conser- 

 vation of momentum and of energy strikes a livelier key, 

 but it is only when von Helmholtz's papers are reached 

 that the reader can feel that the analysis has really becom e 

 an engine of research. The mode of treatment becomes 

 quite ditiferent. The hydrodynamics and thermodynam ics 

 of real air are the starting point, and equatorial heating 

 becomes a secondary consideration. As each section is 

 developed, and the dynamical effect of the scale of the 

 problem, the equilibrium shapes of atmospheric layers, 

 the wave phenomena that can occur between layers of 

 different density are unfolded, it becomes possible to be 

 enthusiastic as to the service that mathematics can 

 render to this subject. 

 Von Helmholtz himself gives no general system of 

 NO. 1660, VOL. 64] 



atmospheric circulation, but M. Brillouin indicates the 

 results in that direction that flow from his conclusions. 

 He finds them in general agreement with Ferrel's distri- 

 bution, and pays a tribute to Ferrel's achievement on 

 that account. 



The notes throughout are frank, appropriate and 

 useful. It is to be feared that the book appeals to a 

 limited class of readers, namely those who are at the 

 same time meteorologists and mathematicians. The 

 ordinary meteorologist will feel the want of a mathe- 

 matical introduction, and the ordinary mathematician of 

 a meteorological introduction. W. N. S. 



OUR BOOK SHELF. 

 The Elements of the Differential and Integral Calculus. 

 By J. W. A. Young, Assistant Professor of Mathe- 

 matical Pedagogy in the University of Chicago, and 

 C. E. Linebarger, Instructor in Chemistry and Physics 

 in the Lake View High School, Chicago. Pp. xvii -|- 

 410. (London ; Hirschfeld Bros., igoo.) Price \os. bd. 

 net. 

 Differential and Integral Calculus with Applications for 

 Colleges, Universities, and Technical Schools. By 

 E. W. Nichols, Professor of Mathematics in the 

 Virginia Military Institute. Pp. xi + 394. (Boston, 

 U.S.A.: D. C. Heath and Co., 1900.) 

 The first of these books is based upon the German treatise 

 on the differential and integral calculus with special 

 reference to chemistry which was published by Profs. 

 Nernst and Schonflies five or six years ago. The chief 

 alteration in the mode of presenting the subject is that the 

 method of limits is used throughout in the treatise before 

 us to the exclusion of the method of differentials which 

 was early introduced and much employed in the German 

 text-book. But the distinctive feature of the original 

 work, viz. the continual use of illustrative examples from 

 chemical and physical science, has been retained in the 

 adaptation before us, and many additional examples of 

 the like kind have been introduced. 



The treatise in its present shape forms a very con- 

 venient and serviceable text-book for English and 

 American students of chemistry desirous of obtaining an 

 elementary acquaintance with the principles and methods 

 of the calculus, for here they will find a very clear pre- 

 sentation of the fundamental ideas of the subject, and m 

 particular will be furnished with abundant easy e.xercises 

 and applications of the mathematical processes to sub- 

 jects in which they are specially interested. The book 

 is well designed to save the time and keep up the interest 

 of such students. Thus the first chapter contains an in- 

 troduction to analytic geometry, with numerous exercises 

 on the graphing of curves, and the last chapter is a 

 characteristic one on the differentiation and integration 

 of functions found empirically. 



Whilst so much has been done to smooth the path and 

 provide for the wants of the class of students specially in 

 view, it seems matter for regret that an additional chapter 

 on the solution of easy linear differential equations has 

 not been furnished. 



We have in I'rof. Nichols' work another elementary 

 text-book specially designed as a first book on the 

 calculus for students of physics and engineering. It is 

 a clear and teachable work foi beginners, and contains 

 several easy applications to mechanics and electricity. 

 The ordinary applications of the differential calculus to 

 geometry are brought forward earlier than usual ; thus 

 we have a chapter on tangents, normals and asymptotes 

 to plane curves before the chapters on successive differ- 

 entiation, series, illusory forms and maxima and minima. 

 Then,- after a chapter on partial and total differentiation, 



