Discontimiity in the Phenomena of Badiation 63 



varying by the same amount from any other speed. In fact 

 more than 60 per cent, of the molecules have at a given instant 

 speeds between one-half and twice this speed, and less than 

 1 per cent have velocities more than two and a half times it. 

 For air in normal conditions it is about 460 metres per sec. Of 

 course any one definite molecule will probably assume in its 

 career the most various speeds, but the actual number within 

 defined limits of velocity remains practically unchanged. Further 

 the average kinetic energy of a molecule, that is the total kinetic 

 energy divided by the number of molecules is a definite quantity, 

 which depends on the temperature in a very simple way ; it is 

 simply proportional to the temperature, provided we measure 

 this not from the arbitrary zeros of the usual scales but from the 

 absolute zero. Of course this average kinetic energy per molecule 

 is a very small amount of energy indeed, even at very high 

 temperatures, on account of the excessively small mass of the 

 molecule. It can be obtained by multiplying the absolute 

 temperature of the gas by a fractional number which is nearly 

 200 trillionths (i.e., 2x10"^'^), the units of energy being those 

 suitable to the C.Gr.S. system, viz., ergs. To avoid repeating 

 this extremely small number too much let us indicate it by a 

 letter, say a, and refer to the average molecular kinetic energy 

 of a gas at temperature T on the absolute scale as 

 a T ergs. 

 The application of the same mathematical methods which 

 have proved so successful in the case of gases, to the case of solid 

 bodies is naturally attended with more difficulty, and the positive 

 results are much fewer. As regards the energy of each molecule, 

 however, a result, which is an extension of that for the gas, can 

 be obtained with a considerable weight of evidence in its favour 

 on the basis of ordinary dynamics. It is known as the Theorem 

 of the Equipartition of Energy. Returning to the case of the 

 gas for a moment, the mathematical analysis only coijsiders the 

 energy possessed by the molecule by reason of its general trans- 

 latory motion, with no reference whatever to any internal energy 



