4 o6 SCIENCE PROGRESS 



chemistry. Take, for instance, the vast amount of mathematical 

 juggling that has been done to make the processes of esterifica- 

 tion and hydrolysis fit the theory of ionic dissociation of 

 electrolytes in solution. The unruly and unconformable fact 

 that the molecular catalytic activity of acids decreases with 

 aqueous dilution, while the degree of ionic dissociation must be 

 assumed to increase, has been entirely neglected, though dis- 

 covered by Ostwald as long ago as 1883 and since shown to be 

 true by other observers. To fit this little block into the founda- 

 tion we may have to raze to the ground all the elaborate 

 superstructures erected by Stieglitz, Acree and Johnson, 

 Goldschmidt and others. 



Frequently the errors are more mathematical and the sooner 

 chemists understand clearly the principles and methods of 

 mathematics and can be sufficiently critical, so that they cease 

 treating a mathematical formula as a sort of fetish, the sooner 

 shall we be able to relegate to its proper place — the waste-paper 

 basket — a very large part of the mass of mathematical investiga- 

 tions of chemical problems foisted upon a credulous public 

 of late years. What is needed is a sort of cupellation process 

 for chemical mathematics which will remove the lead and leave 

 the little silver that is in the ore. 



With regard to the actual requirements of the chemist in the 

 matter of mathematical training, a few personal opinions based 

 on considerable experience may serve to induce discussion or 

 criticism. What is most essential is not so much the skill of 

 deducing and using mathematical formulae and of carrying out 

 certain mathematical processes (which a chemist can, if neces- 

 sary, get a mathematician to do for him) as a thorough drilling in 

 the principles, methods and application of mathematics. This 

 should form a most useful supplement to his chemical training 

 and endow him with a power of reasoning which is definite and 

 exact — in comparison with which his chemical mode of thought 

 is vague and incomplete, dealing as it so often must with 

 problems that are highly and obscurely complex and which 

 cannot at present be subjected to exact mathematical treatment. 

 Without this training, all the mathematical agility a chemist 

 may acquire is likely to be worse than useless. But this is just 

 where not only books but the general attitude of physical 

 chemists towards mathematics seems deficient. Chemists are 



