﻿Thermions from the Salts of the Alkaline Earths. 125 



since the coefficient of potential between the two systems is 

 not zero. The steady deflexion acquired by the electrometer 

 will not, therefore, be exactly proportional to i 2 t. When 

 the connexion S is dropped into place the parts of the charges 

 i L t and i 2 t to the right of R are mixed and the electrometer 

 indicates a new potential resulting from the readjustment. 

 This new potential is not, however, exactly proportional to 

 {i 1 + i 2 )t, since the fraction of this charge left on the parts of 

 the system to the left of R is a variable depending upon the 

 relative values of ij and i 2 . The ratio of the two readings of 

 the electrometer, say 6 2 l@, is not, therefore, exactly pro- 

 portional to i 2 /(/i-f- h)- It ma y be easily shown, however, that 

 a maximum in is/(h + ia) will be correctly indicated by a 

 maximum in 6 2 jQ , and this alone is of importance in these 

 measurements. 



We shall now inquire how the displacement of this 

 maximum by a magnetic field is related to ejm for the carriers 

 and to the other physical quantities involved. If, in fig. 1, 

 we choose the direction parallel to the plane A A and at 

 right angles to the strip as the ^-direction in a system 

 of Cartesian coordinates, the direction normal to AA as the 

 //-direction, and that parallel to the strip as the ^-direction, 

 any ion moving in the space between the two plates will 

 satisfy the three differential equations: 



d 2 x f v TT dy TT dz 



de 1 + *dt 'dt 



where X, Y, Z are the components of the electric field in 

 electromagnetic units, and H x , H y , H z are the components 

 of the magnetic field in gausses. 



The disposition of apparatus is such that 



Y=Z = H x =H,=0, 



and X=Y/d, 



where V is the difference of potential between AA and BB 

 and d is the distance between them in centimetres. 



Since the laws of emission of the ions from a heated 

 surface are known, the current density at any point of tin 4 

 plane BB is determinate, and the calculation of ts/(i'i + t s ) is 

 theoretically possible. Practically, however, the problem 



qsw 



