380 On the Chemical Combination of Gases, 



not noticed that the paired time is inversely proportional to 

 the number of atoms, I must endeavour to find some way of 

 explaining myself which shall not entail the necessity of form- 

 ing any abstract conceptions. Let us then illustrate the 

 pairing of a molecule by the act of getting into a cab, and a 

 gas by a number of men and cabs, the men riding about in the 

 cabs, getting out, and after walking about for a time getting into 

 a cab again. To fix our ideas, let us suppose that after leaving 

 a cab, each man gets into the sixth cab he meets. Then it is 

 evident that the time he spends on foot (his " free time ") 

 will depend upon the number of cabs, the more cabs the 

 shorter the time ; and if the cabs are evenly distributed, his 

 " free time " will be inversely proportional to the number of 

 cabs. But after getting into a cab, unless he is upset by a 

 collision with another cab, there is no reason why the time 

 he stays in his cab should depend upon the number of cabs. 

 Prof. Ostwald's remark, when applied to this case, is — it 

 is difficult to conceive how it is that I have not noticed that 

 the only way of getting out of a cab is to wait until one is 

 shot out by the collision of one's own cab with another. But 

 difficult as the conception is, Prof. Ostwald is equal to it, for 

 in a footnote he suggests that the reason is that I knew 

 what the result ought to be, and so " cooked "" my equations 

 accordingly. Now I should not have thought it worth while 

 to reply to criticism of this order had it not been that the 

 subject of the application of mathematics to chemistry is only 

 dealt w T ith in a few text-books, so that it is important to point 

 out any misrepresentations and misstatements in those which 

 profess to explain this subject. The amusing part of Prof. 

 Ostwald's criticism is that when, after his tirade, he attempts 

 to obtain one of my equations, he implicity assumes that the 

 molecules are not split up by the collisions, for he assumes 

 that the number of molecules split up in a given time is pro- 

 portional to the average number of molecules. Now, if we 

 refer to the illustration of the cabs, it will be evident at once 

 that this is equivalent to assuming that the collisions have 

 nothing to do with the breaking-up of the molecules, for if 

 the men were shot out of their cabs by collisions with cabs 

 with men inside, the number leaving their cabs in any time 

 w T ould be increased fourfold if the number of men in cabs 

 were doubled, for the number of men in cabs would be 

 doubled, and the average time they spend in the cabs would 

 be halved. 



It may illustrate the care with w r hich the book has been 

 written, and the reliance to be placed on its contents, if I 

 mention that within about half a page Prof. Ostwald makes 

 three misstatements. He says that an equation he obtains by 



