218 SCIENCE PROGRESS. 



an impact will take place, for others not, calculate the 

 average value of the repulsive impulse per encounter, and 

 multiply by "s" the distance at which it takes place. The 

 result will be of the same sign as 'Emit 2 . 



29. Tait's reasoning is as follows : The increase of 

 Emu 2 , depending as it does on the number of molecules 

 in entanglement at any instant, is proportional to the 

 number of encounters. Now for given volume this is pro- 

 portional to the square of the density, but for a given num- 

 ber of molecules proportional to the density only, and there- 

 fore inversely proportional to v. He therefore adds to Kt 



c 



or E, the term where C is positive, and y of uncertain 



sign. In like manner for the two parts of EERr he writes 



A , A / C \ , 



— — - and — — Kt + — — ) (part iv., p. 265). I see no ob- 



jection to this reasoning except that it falls short of Professor 

 Tait's own standard of perfection, because it introduces five 

 disposable constants while the theory allows only three. 

 That, of course, does not detract from the value of the 

 formula as an empirical formula, a concession to the weak- 

 ness of the flesh. And certainly for the values of the con- 

 stants assumed, p. 271, the formula gives results agreeing 

 remarkably with those of Amagat. Does it not agree with 

 them more closely than is necessary, considering that the 

 calculated results are, in the matter of the constant r, only 

 approximate ? 



30. The relation between kinetic energy and temperature. 

 In the original or elastic sphere form of the theory we are 

 compelled to treat kinetic energy of translation as identical 

 with heat, and as a measure of temperature, because it is 

 the only form of energy which we allow our system to pos- 

 sess. When we give our molecules many degrees of free- 

 dom, and as many forms of kinetic energy, the question 

 arises, which of the corresponding forms of energy measures 

 temperature ? We quieted our consciences for a time by 



KX 2 -I- V 2 -4- Z 2 ) 3 



the law m — ~ — = - , saying that it did not matter 



1 n J & 



which, because all that is required is a measure, and accord- 



