Contact Potential and Thermionic Emission. 557 



with its necessary (automatic) appearance in (np } , npi) ; it is 

 one main connecting link between the original vectors and 

 those obtained by inversion (crossed pairing). The perpen- 

 dicularity of (M, s), requiring equal orthogonal projections 

 upon the line or! (s) for the vectors (Q 2 , Qa'O? considered by 

 itself demands no more than equality of scale-factors applied 

 to the same segment of that line. The consideration that here 

 precedes makes the selection (ws) natural. 



The material of this particular discussion traverses familiar 

 ground, so far as the final facts about conjugate vectors are 

 concerned. But the line of attack there formulated is capable 

 of deducing novel results elsewhere. 



University of California. 



LXIV. Contact Difference of Potential and Thermionic Emis- 

 sion. By 0. W, Richardson, F.R.S., Wheat stone Pro- 

 fessor of Physics, and F.S. Robertson, M. I. E.E.' Lecturer 

 in Electrical Engineering, University of London, King' 's 

 College *. 



IT has been pointed out by one of us f that the following 

 relation should subsist between the contact potential 

 difference V between two surfaces at the absolute temperature 

 T and their thermionic electron saturation currents i ± , i 2 per 

 unit area at the same temperature : — 



VIC J_ n 2 o 

 = — log- (1) 



e i 1 v ; 



In this equation, h is Boltzmann's constant and e the elec- 

 tronic charge. 



Observations which confirm the validity of this equation, 

 approximately at any rate, have been made by us in the 

 course of some experiments with a thoriated tungsten filament. 

 The filament was o"f tungsten containing 1 per cent, of thorium 

 and was kindly supplied to us by the Tungsten Manufacturing- 

 Co. Ltd., 231 Strand, London. It was 3*0 cm. long and 

 O'lOO mm. in diameter, and was mounted axially in a cylin- 

 diical glass tube and surrounded by a coaxal copper anode. 

 The general arrangements for evacuation and for controlling 

 the temperature of the filament, etc., were similar to those 

 described in our paper on the effect of gases on the contact 

 difference of potential between metals J. After baking out 



* Communicated by the Authors. 



t 0. W. Richardson, Phil. Mag. vol. xxiii. p. 265(1912); and ' Emis- 

 sion of Electricity from Hot Bodies/ p. 41. Second Edition (1916). 

 X Phil. Mag. vol. xliii. p. 162 (1922). 



