762 Sir J. J. Thomson on 



tbe coefficient of mutual induction for these coils had been 

 carefully determined by Mr. Searle ; (2) by means of a 

 D ml dell induction-meter which had been standardized at the 

 National Physical Laboratory and which was kindly lent to 

 me by the Cambridge Scientific Instrument Co. The two 

 methods gave results agreeing within less than 1 per cent, 



With regard to the electrostatic deflexion we have to allow 

 for the irregularity of the field near the edges of the plate ; 

 the case is one for which a complete solution is given by the 

 Schwartzian transformation 



l Jt = C T+i where * = *+M 



or x + iy = 0(t - log (1 + 1) + iV), 



dw B , , . 



Tt=t+l where » = ++»+. 



or $ + fy = B{log(l + <)— wrl, 



where y — Ctt is the equation to one plane and y = — CV 

 to the other, y — is the plane midway between them ; 

 \jr is the potential and <£ the current function, 2Btt the 

 difference o£ potential between the plates. The range of t 

 over one of the semi-infinite planes and the plane midway 

 between them is shown in fig. 9. t ranges from + co to 

 on the upper, from t &= to — 1 on the lower surface of the 



Fig. 0. 



*=?° £l-/ 



semi-infinite plate, and from £=— 1 to t=— co on the 

 plane midway between the two plates. 



We shall suppose that the undeflected path of the particle 

 is in this median plane. The equation of motion is 



tfy 



dV 



a V v 



or approximately mv 2 -~~ = Ye, 



where Y is the electric force perpendicular to the plates, 



Y — drf — ^4* 

 dy dz ' 



