Heat produced by Emission of Ions from Hot Bodies. 635 

 We see also from (9) and (10) that 



aR*+dR/ Dt + IV 

 dR e " D E ' 



Thus 



.... (12) 



Of the quantities on the right-hand side R*/e is a known 

 constant, i u T, T' , D T , D?', D E , R, and # were measured 

 daring the experiments, and ir, a, and y were known. Their 

 values were 7r=*01, a?=l ohm, 3/ = 100 ohms. 6 was only 

 estimated, but its value does not matter much as the term 



R* 



2 — (0 — o ) amounts only to about 5 per cent. o£ <f>. The 



term — — '-H varies from about 5 per cent, to about 



or 



10 per cent, in the different experiments. The value of 3.R e 

 is readily obtained from the corresponding deflexion D E of 

 the galvanometer G bv using the theory of the Wheats tone's 

 bridge circuit. With the resistances and galvanometer used 

 the appropriate relation is 



3R e = l-30x 10- 8 x(G + 100R(l-01 + 0-001G)) x D E . (13) 



It will be observed that the bolometric measurement of 

 the cooling effect due to the thermionic current and the 

 measurement of the Joule heating effect due to a small 

 increase of the main current, are not made under quite the 

 same conditions. The thermionic cooling all occurs at the 

 surface of the filament, whereas the Joule heat is produced 

 uniformly throughout the volume. The mean difference of 

 temperature developed by a given supply of energy will, 

 therefore, be smaller in the latter case, on account of the 

 temperature gradient which is required to drive the energy 

 to the surface of the filament. By considering an analogous 

 case, in which there is no radiation but the loss by radiation 

 is represented by conduction through a surrounding con- 

 ductor of much lower thermal conductivity than the filament, 

 it becomes clear that the error thus introduced is a negligible 

 fraction of the change of temperature which is measured. 



