394 SCIENCE PROGRESS 



be vastly more satisfactory if the necessary parts of mathematics 

 were taught without attempting to deal with chemical problems, 

 with sufficient examples and exercises to make the student 

 proficient in the carrying out of the various processes and if 

 afterwards real chemical problems were dealt with thoroughly." 

 This can only be taken as meaning that the chemical student is 

 to have the following mathematical training : 



(i) A course in pure mathematics, without any indication as 

 to what sort of use the material he is learning is afterwards 

 likely to be to him ; and (2) another course in which the material 

 is applied to chemical problems and in which the student is more 

 particularly told what he is not to do with his previously 

 acquired knowledge. 



Now the first course corresponds with that which the chemical 

 student has been accustomed to receive ; it is one of those " un- 

 necessary and unnatural obstacles " against which he has been 

 "struggling" and is all the less likely to be of real service for 

 the reason that "the chemical and mathematical habits of mind 

 are incompatible " and that " chemists as a class are never likely 

 to be mathematicians." It is my own opinion, supported by the 

 educational teachings of Herbart, that a mathematical process can 

 be most readily assimilated by such persons when it is presented 

 along with some chemical problem, just as the physical student 

 most readily learns the Calculus of Variations in connexion with 

 the Principle of Least Action, Fourier's series and integrals in 

 their application to the Conduction of Heat and the theory of 

 Probabilities as it appears in the Kinetic Theory of Gases. In 

 a text-book of mathematics in which the aim is to teach mathe- 

 matics and not chemistry, nothing can be gained by making the 

 examples too complicated. We do not usually begin our text- 

 books on dynamics by considering the effects of friction or 

 elasticity; nor in teaching the student the theory of conduction 

 of heat do we insist on his trying his feeble strength directly on 

 an irregularly shaped and irregularly heated heterogeneous mass 

 cooling in draughts of air of various temperatures moving at 

 random over its surface, i.e. on real problems. Are we then to 

 be accused of deliberately trying to give " the impression that 

 (physical) problems are very much simpler and straightforward 

 than is really the case " ? I believe that Mr. Worley's accusation 

 that I have tried to do this in connexion with chemical problems 

 is unjust. It is true that in the book the simpler cases of mass 



