242 



Mr. G. W. AValker on the 



In the ordinary method of working Vj is actually zero, and 

 y2 only slightly greater than zero, while Vg is comparatively 

 We thus have approximately the formula 



high 



{F^2b^r^'}e = a,{Y,-Y,)Y, 



(3) 



If 



This equation exactly represents the results in Bartel's 

 electrometer, and shows that if ^2 is positive there will be a 

 maximum sensibility depending on the potential of the needle. 

 The higher the attempted sensibility, by reducing F and 

 increasing V3, the more important does the term ^2^3^ become. 



Can we then account for a positive A'alue of Z/g ? 



Let us consider how C33 varies with the displacement, 

 there were no air-gap between 

 the quadrants, it is clear that 

 C33 would remain constant in 

 all positions of the needle, but 

 in practice the air-gap is not 

 negligible. For example, sup- 

 pose the quadrants are 5 cms. 

 radius, and the air-gap 1 mm. 

 wide, then the ratio of the 

 air-gap to the area of the 

 quadrants is about 2 sq. cms. 

 to 75 sq. cms. 



The capacity of the needle 

 C33 will thus vary, depending 

 on the number of lines of force which escape the quadrants. 



We clearly have stationary values at ^ = and 0-- 

 BC33 



or 



-dO 



= for ^ = and 0^ 



First suppose the angle of the needle 90°. Then as we 

 move from the position ^ = both edges of the needle 

 approach an air-space, and therefore C33 diminishes. It will 



continue to diminish to ^=t? ^vhere it is least. The curve 



will therefore be as shown in fig. (1), and the quantity ^2 is 

 positive. 



Second, suppose the needle to be a mere wire, then C33 



TT 



continually increases from ^ = to ^ = , and the curve is 

 as shown in fig. 2. 



In this case 62 is negative. For angles of the needle near 

 90° we may therefore suppose that 63 is H- , while it is probable 



