Electromagnetic to the Electrostatic Unit of Electric Quantity. 285 



consequently all the numbers obtained for v prior to June 18, 

 1878, we rejected. We now built up two little magnetic balls, 

 each consisting of twenty little magnets, previously magnetized 

 to saturation and slightly separated from one another with pieces 

 of zinc : in each ball all the magnets pointed one way ; and 

 the two balls were used to form an astatic needle. As it would 

 have been difficult to make the entire sphere all of magnets, 

 we finished it off with segments cut from a wooden sphere. 

 Now these magnetic spheres gave us an astatic arrangement 

 of considerable sensibility and without very much damping, 

 the decrement, or the ratio of one swing of the galvanometer- 

 needle to the next, being 1 # 274. About June 18 we made 

 experiments using this astatic combination ; but fearing that 

 even this decrement was too far from unity, we took the needle 

 down in the interval between the 18th and 23rd, and replaced 

 the segments of the wooden sphere by segments of a small 

 leaden hemispherical shell, thus getting a considerable moment 

 of inertia without much extra weight on the fibre. The decre- 

 ment was now found to be diminished to 1*1695 ; and with a 

 periodic time for the swing of the needle equal to 39*5 seconds 

 very consistent results were obtained. 



It might at first appear that the amount of damping action 

 was not very important provided it was known, seeing that 

 Professor Clerk Maxwell gives, on p. 348 of his ' Electricity 

 and Magnetism,' the complete formula for determining the 

 capacity of a condenser by the swing of a galvanometer- 

 needle with any amount of damping. In reality, however, this 

 formula is developed on the assumption that the resistance of 

 the air is for slow velocities directly proportional to the velo- 

 city ; but since we know for large velocities it is proportional 

 to the square, or higher powers, and since the law is not, of 

 course, discontinuous, the resistance even for low velocities 

 cannot be accurately proportional to the velocity ; hence the 

 only way to get perfectly correct results is to diminish the 

 retardation arising from the air or other causes to nearly nil. 



5. Method of Experimenting. 



A current from 382 perfectly new porous pot Daniell's 

 cells in series was passed constantly through a resistance A B 

 (fig. 4) : the difference of potentials at two points, A, C, was then 

 employed to send a current through the shunted galvanometer 

 and through a known resistance R ; and the deflection obtained 

 was, say, d x . Without in any way altering the adjustment of 

 the galvanometer, the connexions were then arranged as in 

 fig. 5. By means of the key K, the upper plate, U, of the con- 

 denser could be connected either with one pole of the battery 



