Heating Effect of Radium and its Emanation. 321 



an a particle causes a recoil o£ the residual atom, the kinetic 

 energy of the latter should he included in the calculation. 

 If ?n, M be the masses of the a particle and recoil atom 

 respectively, and u, U the corresponding velocities, mu = MIT, 

 and the kinetic energy of the a particle and recoil atom 



is given by ^mu 2 l 1-f ^ ). The ratio m/M is slightly less 



than *02, so that the heating effect due to recoil is about 

 2 per cent, of that due to the oc particle itself. 



When the emanation is in transient equilibrium with its 

 products, it has been shown * that radium C is in excess of 

 the true equilibrium amount by 0'89 per cent., so that a 

 slight correction is necessary for this factor. The velocity u 

 of the a particle is deduced from the relation found by 

 Geiger, ?t 3 =.KR, where R is the range in air. Taking the 

 ranges of the u particles from the emanation and its products 

 given by Bragg and correcting for the factors mentioned 

 -above, it can be simply shown that the heating effect of the 

 emanation in transient equilibrium with its products is 

 distributed as follows: — 



Emanation ... 28*8 per cent. 

 Radium A ... 30*9 „ 

 Radium C ... 40*3 „ 



The experimental values observed are 29, 31, and 40 

 per cent, respectively, and thus appear in good accord with 

 theory. 



In this comparison no account is taken of the heating- 

 effect contributed by the (3 rays from radium B and radium C. 

 From experiments described later, it appears probable that 

 the J3 rays from these two products contributed under the 

 experimental conditions about 4 per cent, of the total heating- 

 effect. It follows that the percentage of the heating effect 

 included under radium C should be 42' G per cent, instead 

 of 40-3. 



As the result of a number of observations, the heating 

 effect due to radium B + C was found to be certainly not 

 greater than 40*5 per cent, and probably nearer 40*0 percent. 

 It thus appears that radium C provides slightly less heating 

 effect than that to be expected theoretically. While the 

 difference between observation and calculation is not large, 

 it may prove to be significant: for in making the calcu- 

 lations no account is taken of the heating effect of the 

 p rays or of a possible small heating effect due to radium B. 



* Kutherford and Chadwick, Proc. Phys. Soc. xxiv. p. 141 (1912). 



