January 10, 1913] 



SCIENCE 



63 



SCIENTIFIC BOOKS 

 Higher Mathematics for Chemical Students. 



By J. E. Partington. New York, D. Van 



Nostrand Co. 1912. 



A first question is : Do chemists need any 

 higher mathematics ? And it must be admitted 

 that the inorganic analytical chemist, the or- 

 ganic synthetic chemist, the agricultural 

 chemist, and a host of others, by a large mar- 

 gin the majority of all, do not need much, if 

 any, mathematics, and perhaps a quarter cen- 

 tury ago no chemist was much the better off 

 for a knowledge of the subject. Of late, how- 

 ever, there has been a great development of 

 physical and dynamic chemistry, wherein 

 mathematical methods are of great impor- 

 tance, so that there has come considerable de- 

 mand for mathematics from a large and grow- 

 ing class of theoretical chemists, and the de- 

 mand is likely to increase in the future. In- 

 deed if a student desires to read such mem- 

 oirs as that of Gibbs on the equilibrium of 

 heterogeneous substances, he must have a 

 tolerably thorough foundation in some 

 branches of mathematics. 



A second question : Is there any necessity 

 for a special treatment of calculus for chem- 

 ists? The appearance of such works as 

 Mellor's " Higher Mathematics for Students 

 of Chemistry and Physics " and this work of 

 Partington's would seem to imply that there 

 was. And the publication of special texts for 

 engineers, economists and the like is evidence 

 that others than chemists feel such a need. 

 In this connection we may cite the excellent 

 address by C. Eunge at the International Con- 

 gress of Mathematicians in Cambridge last 

 summer on the university training of the 

 physicist in mathematics. It is there pointed 

 out with force, but kindness, that our mathe- 

 maticians do not organize their course of in- 

 struction with sufficient reference to the ad- 

 vantages of the great majority of their stu- 

 dents, namely, those who are going into phys- 

 ics, chemistry, economics, engineering, and, 

 indeed, anything except pure mathematics — 

 and in so organizing them they are not ma- 

 king for any very preponderating advantages 

 for the few students of pure mathematics. 



The sort of course in calculus that the ele- 

 mentary student of applied mathematics should 

 have is one where the ideas and methods of 

 differential and integral calculus, including 

 differential equations, are .most fully empha- 

 sized and thoroughly illustrated by simple 

 formal work applied to a great variety of prob- 

 lems. For it must be remembered that nine 

 tenths of the problems where the student will 

 use his calculus can be treated with the sim- 

 plest sort of analysis. So long as mathemati- 

 cians insist upon a training in differentiation 

 and integration which requires the exercise of 

 a considerable amount of advanced algebra 

 and analytical trigonometry, the student of 

 the elementary applications will find himself 

 burdened with unnecessary material which 

 may be hard for him and which can not fail to 

 distract his attention from the work he most 

 needs. And just so long there will be at- 

 tempts, justifiable attempts, to compile trea- 

 tises out of the line of the regular mathemat- 

 ical courses for the use of such' students. 



Whenever a book thus intended for a special 

 class appears it must be judged from a double 

 point of view : First, how is it as mathematics ; 

 second, how does it meet the needs of that 

 special class? 



Judged from the point of view of the mathe- 

 matician, Partington's work is far from good; 

 it has that sort of inaccuracy which indicates 

 that its author, no matter how much he may 

 use his mathematics, does not have any thor- 

 ough knowledge of the subject; it abounds in 

 the kind of glaring crudities with which every 

 serious teacher is familiar on the part of his 

 pupils and which he seeks constantly to elimi- 

 nate, though often unsuccessfully, from their 

 minds. A few instances must be cited to 

 justify so sweeping a condemnation. 



On page 21 in the definition of limit the 

 statement that the variable can never reach 

 its limit is incorporated. With the artificial 

 discontinuous variable of elementary geometry 

 this is true, though unessential; with the con- 

 tinuous variables of physics it is not true. On 

 page 31 in varying the equation pv = E by 

 assigning increments to the variables the au- 

 thor writes 



