Electromagnetic to the Electrostatic Unit. 305 



much more would their sum be so. I therefore conclude that 

 the difference of the observed capacities of condenser and 

 charging system together and of charging system alone is a 

 true measure of the capacity of the condenser. 



•i. Displacement of the hall. — The upper half of the spheri- 

 cal shell was lifted and the lower half adjusted upon its sup- 

 ports until the distance of the ball from the shell was the same 

 at all points on the equatorial circumference. The upper half 

 of the shell was then replaced, and by means of the rack and 

 pinion the ball was first lowered and then raised until it 

 touched the shell, the exact moment of touching being indi- 

 cated by an electrical contact, and several readings taken on 

 the vernier in each position. The mean of the readings in the 

 two positions gave the central position. In this manner the 

 ball was adjusted vertically to within 01 mm. and equatorially 

 within 0*2 mm. Thus the ball is centered to within less than 

 one per cent of the distance between the ball and shell, which 

 is 25 mm. Thomson has investigated a formula for the capa- 

 city of eccentric cylinders. The formula shows that for a dis- 

 placement of one per cent the capacity is increased ^r^th of 

 one per cent. Evidently the capacity of spherical shells is less 

 affected by slight eccentricity than cylinders. Therefore we 

 may safely conclude that no error is due to eccentricity. This 

 conclusion was verified experimentally, a displacement of four 

 per cent causing an inappreciable change. 



5. Adjusting resistances. — The accidental errors occurring 

 in adjusting the resistances a so as to produce zero deflection 

 will be eliminated by a large number of observations. Their 

 magnitude depends on the strength of the current, delicacy of 

 the galvanometer, regularity of the vibrator, etc., and are larger 

 with the slow fork than with the fast. The stronger the cur- 

 rent and more sensitive the galvanometer the greater the de- 

 flection due to a certain error in a, but on the other hand the 

 greater the unsteadiness of the spot, so there is a practical limit 

 in that direction. That these accidental errors are small is, I 

 think, attested by the uniformity of the results obtained. 



, ' Electrostatic capacity. 



The electrostatic capacity of the condenser was calculated 



from the formula C = >, where r, r' are the radii of the 



shell and ball respectively. The radii are determined by find- 

 ing the volume of water which fills the shell and which is dis- 

 placed by the ball. These results are confirmed by direct 

 measurement upon the dividing engine. 



Am. Jour. Sci.— Third Series, Vol. XXXVIII, No. 226.— October, 1889. 

 20 



