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'■■., 



LXII. The Absorption of Heat 'produced by the Emission of 

 Ions from Hot Bodies. By H. L. Cooke, Assistant Pro- 

 fessor of Physics, and 0. W. Richardson, Professor of 

 Physics, Princeton University *. 



IN 1903 f one of the writers pointed out that there should 

 be a considerable stream of energy away from the 

 surface of a hot body which is emitting electrons or ions. 

 When the total thermionic current is i the rate of loss of 

 energy is 



z(<£> + 2-0! m 



•'(* + 2 7*)' (I 



where <S> is the drop of potential through which an ion 

 would have to fall in order to acquire the energy which is 

 equal to the heat rendered latent when the ion is emitted by 

 the substance, R is the gas constant for a single molecule, 

 e is the charge on an ion, and 6 is the temperature of the 

 substance. Since i increases very rapidly with 0, the rate 

 of loss of energy due to this cause should also increase very 

 rapidly with increasing temperature. 



In the paper referred to, the derivation of the formula 

 which is equivalent to (1) is confined to the case of the 

 emission of electrons, and is based upon the electronic theorv 

 of metallic conduction. The scope of the formula is, however, 

 much wider than this. It can, in fact^ be shown to hold for 

 any case in which it is possible to have equilibrium between 

 an external atmosphere of ions and the source of emission. 

 Strictly speaking, these statements are only universally true 

 provided the phenomenon of electron reflexion is disregarded. 

 The modifications which may have to be introduced on this 

 account cannot be large and will be referred to later. 



Attempts to detect and measure this loss of energy have 

 been made by Wehnelt and Jentzsch J and by Schneider §. 

 These investigators all used a lime-coated platinum wire as 

 the source of electrons. They agree in observing a coolino- 

 effect which is generally larger than that given by the above 

 theory. The discrepancy is most marked at the lower tem- 

 peratures, where Wehnelt and Jentzsch believe their results 

 to be most reliable. At the higher temperatures there is a 

 considerable emission of gas from the heated wire, and this 

 is ionized by collision with the escaping electrons ; the 



* Communicated by the Authors. 



f O. W. Richardson, Phil. Trans. A. vol. cci. p. 502 (1903). 



X Ann. der Phys. vol. xxviii. p. 537 (1909). 



§ Ibid. vol. xxxvii. p. 569 (1912). 



