Negative Corpuscles by the Alkali Metals. 589 



energy into the kinetic energy of corpuscles and a particles, 

 but in this case, as far as is known, the transformation is 

 quite uninfluenced by external physical conditions, and is 

 thus beyond our control. If, however, the view we have 

 been considering above is correct, the tapping of the internal 

 atomic energy by corpuscular streams is to some extent 

 under our control and can be brought about by elevation of 

 temperature or by ultra-violet light. 



Since the emission of corpuscles goes on to some extent at 

 all temperatures, and since inside a body the energy of these 

 corpuscles would ultimately be transformed into heat energy, 

 there is probably a continual transformation of internal 

 atomic energy into heat: this would cause the interior of a 

 mass of metal to be hotter than the surface, the increase in 

 the inside temperature depending on the amount of energy 

 transformed, on the size of the body, and on its thermal 

 conductivity. 



If the body is a sphere of radius a, of uniform composition, 

 we can easily show that #, the difference between the tem- 

 perature of the surface and that at the centre, is given by the 

 equation 



where q is the amount of energy transformed into heat 

 per cubic centimetre per second, k the thermal conductivity 

 of the substance. 



For bodies comparable in size with the earth, a very 

 small amount of transformation of internal atomic energy 

 into heat would produce very large differences of tem- 

 perature between the centre and the surface. Thus, if the 

 conductivity of the sphere were *01, which is about three 

 times that of granite at the temperature of the earth's 

 surface, there would be a difference of 3000° C. between the 

 centre and surface of a sphere the size of the earth if 

 (/ = 45xl0~ 17 , i. <?,, if the atomic energy transformed into 

 heat per c.c. in 100 million years were less than that required 

 to raise the temperature of 1'5 gramme of water 1° G. If 

 the corpuscles were emitted with a kinetic energy corre- 

 sponding to that which would be acquired by the fall of their 

 electric charge through two volts, the emission by an atom 

 of a corpuscle once in a thousand million years on an 

 average would be far more than sufficient to produce the 

 required transformation of energy. The temperature differ- 

 ence between the centre and the surface being proportional 



