214 PROFESSOR E. RUTHERFORD ON THE 



per second from 1 gramme of radium in radioactive equilibrium. This estimate li;is 

 been deduced as an average of three distinct methods of calculation based on 



(1) The charge carried off by the rays ; 



(2) The energy required to produce an ion ; 



(3) The number of ions produced per centimetre of path by an a particle. 



A check on this estimate can be made from calculations of the heating effect 

 observed in radium. There is little doubt that the heating effect of radium is due 

 mainly to the bombardment of the radium by the a particles expelled from its 

 substance. Now, since e/m = 6'3 x 10 3 for the a particle, and the velocity v is 



2'5 X 10 9 , the kinetic energy of the a particle is fytnv 1 = J . v 1 . e 6 X 10~ 6 erg, 







if the charge e = 3 '4 X 10~ 10 electrostatic unit. 



The rate of heat emission from 1 gramme of radium is equal to 100 gramme-calories 

 per hour, i.e., is mechanically equivalent to 1'2 X 10 6 ergs per second. If the 

 heating effect is supposed to be due to the kinetic energy of the expelled a particles, 

 2 X 10 11 a particles must be expelled per second to account for the heat emission. 

 This number is in good accordance with the calculated estimate already given. 

 Knowing the number of a particles expelled per second, the volume of the emanation 

 stored up in 1 gramme of radium can at once be deduced. For the purpose of 

 calculation, it is assumed that each atom in breaking up gives rise to one a particle 

 and to one atom of the succeeding product. This is supported by the observed result, 

 that each active product of radium supplies almost an equal proportion of the total 

 activity measured by the a rays, i.e., each active product expels about the same 

 number of i-ays. Now, a rays are expelled by the radium itself, by the emanation, and 

 the products radium A and C. The amount of the slowly changing products radium 

 D and E present is too small to take into account. There are thus four a particles 

 expelled for each radium atom which breaks up. There are thus 2'5 X 10 10 atoms ot 

 radium breaking up per second. In a state of radioactive equilibrium the number n 

 of atoms of emanation present per gramme of radium is given by n/q = I/A, where q 

 is the number supplied per second, or the number of radium atoms breaking up per 

 second, \ is the radioactive constant. Since I/A = 500,000 for the emanation, and 

 q = 2-5 X 10 10 , we have n = 1'25 X 10 16 . TOWNSEND showed that Ne = T21 x 10 10 , 

 where N is the number of molecules of hydrogen per unit volume at atmospheric 

 pressure and temperature. 



Taking J. J. THOMSON'S value of e, 3 '4 X 10~ 10 electrostatic unit, we find 

 N = 3'6 X 10 19 . The volume of the emanation from 1 gramme of radium is n/N cub. 



1*25 X 10 16 

 centims., which is g , or 3'5 X 10"* cub. centim., at standard pressure and 



O O ^\ -L \J 



temperature. 



Now, RAMSAY and SODDY have recently isolated the emanation, and deduced that 

 the volume from 1 gramme was equal to about 1 cub. nullim. The calculated volume 



