Prof. Thomson on the Measurement of Electrostatic Force. 237 



the second, *$fa of the number of degrees of torsion. The mean of 

 these is .^L, or 1*2 ; and we may consider this number as represent- 

 ing approximately the value in grains' weight at -fa of an inch 

 distance between the discs of the absolute electrometer, correspond- 

 ing to one degree of torsion of the portable electrometer. By com- 

 paring the indications of the portable electrometer with those of 

 the divided ring electrometer, and by evaluating those of the latter 

 in terms of the electromotive force of a Daniell's battery charged 

 in the usual manner, I find that 284 times the square root of the 

 number of degrees of torsion in the portable electrometer is approxi- 

 mately the number of cells of a Daniell's battery which would pro- 

 duce an electromotive force (or, which is the same thing, a difference 

 of potentials) equal to that indicated. Hence the attraction between 

 the discs of the portable electrometer, if at -fa of an inch distance, and 

 maintained at a difference of potentials amounting to that produced by 

 284 cells, is 1*2 grain. The effect of 1000 cells would therefore be 

 to give a force of 14*9 grains, since the force of attraction is propor- 

 tional to the square of the difference of potentials between the discs. 

 The diameter of the opposed circular areas between which the attrac- 

 tion observed took place, was 5*86 inches. Its area was therefore * 187 

 of a square foot, and therefore the amount of attraction per square 

 foot, according to the preceding estimate for -fa of an inch distance 

 and 1000 cells' difference of potential, is 79' 5 grains. To reduce 

 the statement to consistent units founded on a foot as the unit of 

 length, we may suppose, instead of j 1 ^ of an inch, the distance 

 between the discs to be j4» of a foot. We conclude that, with 

 an electromotive force or difference of potentials produced by 1 000 

 cells of Daniell's battery, we find for the force of attraction 55*3 

 grains per square foot between discs separated to a distance of y-J-g- 

 of a foot, 



This result differs very much from an estimate I have made ac- 

 cording to my theoretical estimate of 2,500,000 British electro- 

 magnetic units for the electromotive force of a single element of 

 Daniell's and "Weber's comparison of electrostatic with electro-mag- 

 netic units. On the other hand, it agrees to a remarkable degree of 

 accuracy with direct observations made for me, during my absence 

 in Germany, by Mr. Macfarlane, in the months of June and July 

 1856, on the force of attraction produced by the direct application 

 of a miniature Daniell's battery, of different numbers from 93 to 451 

 of elements, applied to the same absolute electrometer with its discs 

 at '079 of an inch asunder. These observations gave forces varying, 

 on the whole, very closely according to the square of the number of 

 cells used ; and the mean result reduced according to this law to 

 1000 cells was 23 # 4 grains. Reduciug this to the distance y^y 

 of a foot, and dividing by "187, the area in decimal of a square foot, 

 we find 54*3 grains per square foot at a distance of y-J-g- of a foot. 



Although the experiments leading to this result were executed with 

 great care by. Mr. Macfarlane, I delayed publishing it because of the 

 great discrepance it presented from the estimate I deduced from 

 Weber's measurement, which was published while my preparations 



