A TEST FOR ELECTRON POLARIZATION 477 



values found for the deflections correspond to actual differences in the 

 current to the collector, and to attempt to evaluate the amplitude co- 

 efiicient of the polarization effect. We shall find actually that observa- 

 tions at four positions only are insufficient to determine this constant 

 precisely. 



It will be appreciated that differences in the collector current at 

 different angles may arise from mechanical defects in the apparatus — 

 improper alignments, etc. — as well as from polarization, and that in 

 general we shall require for the expression of Z) as a function of a 

 complete Fourier series such as 



D = Dn 



1 + Z! a„ cos (nd -f an) 



1 



The data available for evaluating the constants of this series consist 

 of four values of D, corresponding to the four values of ^ — 0°, 90°, 

 180° and 270°. We designate these four values respectively by Di, 

 D2, D3 and D4. From the four simultaneous equations formed by 

 writing these pairs of values of 6 and D into the series we obtain the 

 following relations: 



D, + D, + Ds-\-D,= 4A 



1 



1 + Zl a4n cos ain , 



Di — D3 = 2Do Z din+i COS a2n+l, 

 



00 



Di — D2 = 2 A Z! (— l)"«2n+i sin a2n+U 







00 



Di — D2 -\- Ds — Di = 4Do Z «4n+2 COS ain+2. 







If we make the definite assumption that all periodic terms of orders 

 greater than the second may be neglected, these reduce to the relations 



D, + D2 + Ds + Di = 4Do, 

 Di — Dz = 2Doai cos ai, 

 Di — D2 = 2Doai sin ai, 

 Di — D2 + D3 — Di = 4:Doao cos 0:2, 



from which we may obtain expressions for ai, ai and ^2 cos 0:2, but 

 not, unfortunately, for 02 and a2 separately; the fourth observation is 

 used up in fixing Do in which we have no interest. Observations at 

 one additional angle would have been sufficient to resolve ^2 and a2, 

 but this was not appreciated at the time the measurements were made. 



