of Steel Needle-Points in Air. 289 



In the same way, /= -, , whence 



Q — 



the value of v being thus independent of the somewhat un 

 certain quantity r. 

 For needle B, 



v = 4' 5 E.S. units for + discharge 

 = 3*3 „ „ — „ 



In order to verify the above values of/ it will be convenient 

 and sufficient to show that these values of v calculated from P 

 are in agreement with those calculated from potential mea- 

 surements. 



The column headed V in Table I. gives the difference of 

 potential in E.S. units between the needle and the plate. 

 Now, except for the presence of the needle itself, the field of 

 force in which it was placed would have consisted of parallel 

 lines ; for the point of the needle was arranged in this experi- 

 ment to project 3 or 4 millim. beyond a flat screen of tin -foil 

 through a small hole in it, and the distance from the tin-foil 

 to the disk (a penny) onto which the needle discharged was 

 small compared with the diameter of the disk, so long as the 

 value of d was less, say, than a centimetre. Even with the 

 needle in position, the field would be disturbed for a very 

 small distance only round about the point, on account of the 

 extreme smallness of the latter. Hence V may be regarded 

 as consisting of two parts — one constant (viz. v) and occurring 

 in a small space close to the point ; the other proportional to 

 d for small values of d. 



Taking the mean of the values of V for each value of d, 

 we obtain the numbers plotted with d in Curves I. The 

 upper curve is for positive discharge, the lower for negative. 

 Up to a distance of something less than a centimetre from 

 point to plate, the values of V lie very fairly on the straight 

 lines ruled through them. V —a constant is thus proportional to 

 d ; and the values of the constants are of course to be found 

 -where the ruled lines cut the axis of V. These points are 

 hardly distinguishable from the. values (which are marked by 

 crosses) of the step of potential at the point calculated above 

 from P (viz. 4'5 and 3*3). They show indeed a slight 

 tendency to exceed these values ; but the agreement is 

 certainly striking, considering the complete independence of 

 the two methods of measurement. 



