288 Mr. A. P. Chattock on the Electrification 



Let da represent an element of area of the point's surface? 

 and 6 the angle between the direction of the lines of force at 

 da and the axis of the needle. Then if the pull on the needle 

 towards the plate be P, 



SttJ- 



f 2 cos 6 da 



over the surface of the point, f being the field-strength at dd* 

 Take now the case of a needle with its point ground to a 

 hemisphere ; and assume (what will not be strictly true) that 

 the value of/ is uniform all over it (see below). Then the 

 above equation becomes 



where r is the radius of curvature of the point. The average 

 value of VP for positive discharge from needle B (Table 1.) 

 is 1*59. That for negative is 1*16. The value of r for so 

 fine a needle is rather uncertain, as it tapers towards the 

 point. Measured under a microscope it seems to lie between 

 1*9 x 10~ 3 and 2*3 x 10~ 3 centim. Taking the mean of these 

 numbers, one obtains the value of the field of force / close in 

 front of the point 



/= V ' 8F = 2140 E.S. units for + discharge, 

 r 



= 1560 „ „ - „ 



The highest measured value of / for discharge in air is, I 

 believe, that obtained by Dr, Liebig for sparks between plates 

 (Phil. Mag. July 1887, p. 106), viz. 400 E.S. units for a 

 spark-length of 0*0066 centim. This is much less than 

 either of the above numbers, but the length of discharge at 

 the point is probably much less than 0°0066 centim. The 

 results may, moreover, be verified by calculation from potential 

 data. 



Although the value of / is so large at the surface of the 

 needle-point, the lines of force diverge rapidly, and at a very 

 short distance from the point the field becomes inappreciable. 

 In other words, there occurs within this short distance a step 

 of potential (v) which, if the point is hemispherical and small, 



may be taken as equal to — , where Q is twice the charge on 



the hemisphere (Q, as already assumed, being uniformly dis- 

 tributed over the point). 



