vit] RADIO-ACTIVE EMANATIONS 24,7 
stored in a non-emanating thorium compound, is only 87 times 
the rate of production, while in radium it is 463,000 times, and the 
rate of production of the emanation by radium is about 1 million 
times faster than by thorium, it follows that the amount of emana- 
tion to be obtained from 1 gram of thorium is not greater than 
10 of the amount from an equal weight of radium, 7.e. its volume 
is not greater than 5x10" cc. at the ordinary pressure and 
temperature. Even with large quantities of thorium, the amount 
of emanation is too small ever to be detected by its volume. 
Heat Emission of the Radium Emanation. 
163. It has been shown in section 106, that the radium 
emanation emits heat at a rapid rate and is responsible for about 
70 °/, of the heating effect of radium. The emanation from 1 gram 
of radium, together with the heat effect due to the excited activity 
on the walls of the containing vessel, thus gives rise to an emission 
of heat of about 70 gram-calories per hour. This rate of heat 
emission decays according to an exponential law with the time, 
decreasing to half value in about four days. The total quantity of 
heat given out during the life of the emanation is 2, where q 1s 
the initial rate of heat production and 2% is the radio-active 
constant of the emanation. Since the value of % expressed in 
hours (section 136) is 1/128 and q is 70, the total quantity of 
heat emitted from the emanation from | gram of radium is about 
10,000 gram-calories. But the volume of this emanation is about 
33 x10-cc. Thus the total heat emitted from one cubic centi- 
metre of the emanation at standard pressure and temperature 
would be about 3 x 10" gram-calories. The initial rate of emission 
of heat is 2 x 10° gram-calories per hour or 60 gram-calories per 
second. This rapid emission of heat would be sufficient to heat 
to redness if not to melt down the tube which contains the 
emanation. 
If the atomic weight of the emanation is taken to be about 200, 
it can be calculated that 1 pound weight of the emanation would 
initially radiate heat at the rate of about 8000 horse-power, and in 
the whole course of its heat emission would radiate an amount of 
