366 SCIENCE PROGRESS 



of those required to account for the Peltier effect. Hence, we 

 may practically write (i) as 



Y-Y' =(!>'- <j> (2) 



if the metals have been put in contact, whether they remain so 

 or are separated. Hence, the contact P.D. of the two metals 

 is thus identified as the difference of their ^ or wje quantities. 

 Suppose, now, we denote this contact P.D. by K and illuminate 

 the first of these metals with light of frequency v, and apply 

 to the other the greatest opposing potential, the " photo- 

 potential," which just allows photo-electric current to flow. 

 Calling this P, we cannot write Ve = hv — w, but 



{V + K)e=hv-w (3). 



or P + K = hl^'v - (f> 



This equation has been very carefully tested in the work 

 of Millikan. It is found to be in excellent agreement with fact. 

 In particular, it has yielded in his hands one of the most precise 

 determinations of Planck's constants. Another feature which 

 has been tested is the connection which it gives between ^ and 

 the " threshold " value of the frequency, i.e. the least value of 



V which just gives any photo-electric effect at all ; the relation is 



hvo = w = (f>e 



Vo is determinable by observation, and j> can be calculated 

 from the application of (3) to measurements of photo-potentials 

 and contact P.D.s. 



Langmuir, in the paper referred to, has pointed out that it 

 is not correct to regard ^ as a P.D. in the usual sense of the 

 term. We define a P.D. as existing between two points, when 

 the work done on an element of charge in transportation is 



V q and the transportation of the hq does not appreciably affect 

 the value of V. But the mechanism of photo-electric and ther- 

 mionic emission seems to be such that the work involved by 

 the removal of a small but finite amount of charge e is due to 

 the back attraction on the e of its mirror image, i.e. its induced 

 charge on the surface of the metal, or the balance of opposite 

 charge left unneutralised by its removal. It can be shown 

 easily, on the law of inverse squares, that the amount involved 

 in removing e from a point distant x from the surface to infinity 

 is ^l<^x, and that if we assume the inverse square law to hold 

 down to a distance Xo, and for nearer distances adopt any 

 plausible hypothesis as to attractive force which does not lead 

 to infinite singularities, then w = ^l2Xo approximately ; i.e. 



If this equation is tested from the known values of 4> and e, 

 it yields quite reasonable values for Xo, all of the order io~^ cm., 



