Method of solving Problems in Conduction of Heat. 603 



the electrometer, as would be expected if radiation and 

 further ionization, respectively, were produced from the 

 ionized atoms at these velocities. Although these results 

 are in agreement with the predictions of Bohr's theory, it is 

 clear that the method of experimenting affords no absolute 

 proof that the observed increase of current does result from 

 such collisions. 



In connexion with the increase of current observed at 

 80 volts, and interpreted as being due to the removal of both 

 electrons from a helium atom at a single electron collision, 

 it might be suggested here also that for some lower electron 

 velocity a single collision should result in the removal of 

 one electron and the displacement of the other to an orbit 

 of oreater radius, thus giving both ionization and radiation. 

 Some experiments by Ran * seem to show that collisions 

 producing an effect of this kind do occur under certain 

 conditions. On the basis of Bohr's theory, the electron 

 velocity at which such an effect would be expected is 25*6 

 volts + | of 54*16 volts = 66'22 volts. We were unable 

 to obtain any evidence of this effect in our experiments. 



The results described in this paper agree with those of 

 Franck and Knipping in showing that the double ionization 

 of the helium atom results from collisions between helium 

 atoms and electrons having about 80 volts velocity, but differ 

 from theirs in indicating bends in the current curves at 

 41 volts and 55 volts which appear to be due to the pro- 

 duction of radiation and of further ionization, respectively, 

 from the helium atoms which have already lost one electron. 



LVIII. Bromwich's Method of solving Problems in the Con- 

 duction of Heat. By Prof. H. S. Carslaw, Sc.I).^ 



1. TN his paper — "Examples of Operational Methods in 

 J Mathematical Physics," Philosophical Magazine, 

 No. 220, April 1919 — Bromwich advocates the use of so- 

 called operational methods, following Heaviside, in electrical 

 and other physical problems, and illustrates his method by 

 the solution of various questions, including some in the 

 Conduction of Heat. In an earlier paper (Proc. London 

 Math. Soc. (Ser. 2) xv. p. 401, 1917) he discussed 

 Heaviside's work, and confirmed it by the aid of contour 

 integrals. 



The object of the present paper is to illustrate by some 



* H. Kaii, Wiirzburg Phys. Med. yes. Ber. Feb. 1914. 

 t Communicated by the Author. 



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