Prof. Thomson on the Measurement of Electromotive Force. 325 



that direction. Since the average electrostatic force in the line joining 

 two points at which the values of the potential are equal, is nothing, 

 the direction of the resultant electrostatic force at any point must be 

 perpendicular to the equipotential surface passing through that 

 point ; or the lines of force (which are generally curves) cut the 

 series of equipotential surfaces at right angles. The rate of varia- 

 tion of potential per unit of length along a line of force is therefore 

 equal to the electrostatic force at any point. 



10. Stratum of air between two parallel or nearly parallel plane 

 or curved metallic surfaces maintained at different potentials. — Let a 

 denote the distance between the metallic surfaces on each side of the 

 stratum of air at any part, and V the difference of potentials. It is 

 easily shown that the resultant electrostatic force is sensibly constant 

 through the whole distance, from the one surface to the other ; and 

 being in a direction sensibly perpendicular to each, it must (§9) 



V 



be equal to - . Hence (§ 4) the electric density on each of the 



y 



opposed surfaces is equal to - — . This is Green's theory of the 



4ira 



Ley den phial. 



11. Absolute Electrometer. — As a particular case of No. 10, let 

 the discs be plane and parallel ; and let the distance between them 

 be small in comparison with their diameters, or with the distance of 

 any part of either from any conductor differing from it in potential. 

 The electric density will be uniform over the whole of each of the 



opposed surfaces and equal to - — , being positive on one and nega- 



tive on the other ; and in all other parts of the surface of each the 



electrification will be comparatively insensible. Hence the force of 



V 2 

 attraction between them per unit of area (§§5 and G) will be - — ^ 



if A denote the area of either of the opposed surfaces ; the whole 



y-2 

 force of attraction between them is therefore A- — ■ . Hence, if the 



oira* 



observed force be equal to the weight of w grains at Glasgow, we 

 have 



32-2 xw=A- 



and therefore 



=v 



87ra*' 

 32-2 X 8tt x iv 



Addition, dated April 12, 1860. 



Experiments on precisely the same plan as those of Table I. 

 December 13, have been repeated by the same two experimenters, 

 with different distances from *3 to *6 of an inch between the plates 



