MATHEMATICS AND CHEMISTRY 403 



practical problems that arise ; unfortunately, they also too often 

 find that the mathematician has not sufficient chemical know- 

 ledge and feeling to give them the assistance they need. Speak- 

 ing on behalf of the mathematician, on the other hand, chemists 

 rarely express their problems properly. They never seem 

 quite clear as to what is to be assumed as known and exactly 

 what is to be proved. Whilst one realises that a mathematical 

 training that would enable and induce the chemist to express 

 his ideas and problems with clear mathematical precision would 

 be of inestimable value, still it must be admitted that chemical 

 problems are frequently of such a nature that it is impossible to 

 be absolutely certain of anything ; the chemist frequently does 

 not know what he wants to prove nor indeed does he want to 

 prove anything ; he wants merely to put a reasonable interpreta- 

 tion upon certain experimental results. 



A still more important question to consider is whether, 

 except in rare cases, the chemical and mathematical habits of 

 mind are compatible — chemical properties are the expression 

 of the reciprocal behaviour of substances, not absolute quanti- 

 ties ; on this account it is very difficult to quantify such 

 properties : often they can be felt but not figured. 



Before dealing with the mathematical requirements of the 

 chemist for the purposes of investigation and research, it is 

 well perhaps to emphasise the great need of giving all chemists 

 a sufficient mathematical training — not much is needed but it 

 must be sound — to enable them to read intelligently and criti- 

 cally the numerous mathematical papers that are continually 

 appearing in chemical journals. To the chemist, such papers, as 

 a rule, are uninviting and often produce a feeling of mistrust 

 and suspicion, especially when, by means that he cannot follow, 

 conclusions are arrived at which are not in harmony with his 

 own feelings. Investigation often shows that these feelings of 

 mistrust and suspicion are unfortunately only too well founded ; 

 there can be no doubt, in fact, that a large proportion of the 

 published mathematical discussions of chemical problems is in 

 need of serious reconsideration. 



The chemist often feels that if only he had the necessary 

 mathematical insight, he would find that the cooking-pot had a 

 paper bottom. As it is his vision cannot penetrate the stew 

 and he perceives only the oily iridescence on the surface or the 

 reflection of nature above. I do not wish to imply that the 



