1864.] 



of Electrical Force. 



365 



is found to depend not only on the surface, but also on its linear boundary 

 extension. Thus the linear boundary of 100 square inches of surface under 

 a rectangle 37'5 inches long by 2*66 inches wide, is about 80 inches ; 

 whilst the linear boundary of the same 100 square inches of surface under 

 a plate 10 inches square is only 40 inches. Hence the charge of the rec- 

 tangle is much greater than that of the square, although the surfaces are 

 equal, or nearly so. 



6. The author finds, by a rigid experimental examination of this question, 

 that electrical charge depends upon surface and linear extension conjointly. 

 He endeavours to show that there exists in every plane surface what may 

 be termed an electrical boundary, having an important relation to the group- 

 ing or disposition of the electrical particles in regard to each other and to 

 surrounding matter. This boundary, in circles or globes, is represented by 

 their circumferences. In plane rectangular surfaces, it is their linear ex- 

 tension or perimeter. If this boundary be constant, their electrical charge 

 (1) varies with the square root of the surface. If the surface be constant, 

 the charge varies with the square root of the boundary. If the surface and 

 boundary both vary, the charge varies with the square root cf the surface 

 multiplied into the square root of the boundary. Thus, calling C the charge 

 S the surface, B the boundary, and some arbitrary constant depending 

 on the electrical unit of charge, we have C = ;uV'S.B, which will be found, 

 with some exceptions, a general law of electrical charge. It follows from 

 this formula, that if when we double the surface we also double the boun- 

 dary, the charge will be also double. In this case the charge may be said 

 to vary with the surface, since it varies with the square root of the surface, 

 multiplied into the square root of the boundary. If therefore the surface 

 and boundary both increase together, the charge will vary with the square 

 of either quantity. The quantity of electricity therefore which surfaces can 

 sustain under these conditions will be as the surface. If I and b represent 

 respectively the length and breadth of a plane rectangular surface, then 

 the charge of such a surface is expressed by ixt>J2lb {l + b), which is found 

 to agree perfectly with experiment. We have, however, in all these cases 

 to bear in mind the difference between electrical charge and electrical 

 intensity (1). 



7. The electrical intensity of plane rectangular surfaces is found to vary 

 in an inverse ratio of the boundary multipUed into the surface. If the sur- 

 face be constant, the intensity is inversely as the boundary. If the boun- 

 dary be constant, the intensity is inversely as the surface. If both vary 

 alike and together, the intensity is as the square of either quantity ; so that 

 if when the surface be doubled the boundary be also doubled, the intensity 

 will be inversely as the square of the surface. The intensity of a plane 

 rectangular surface being given, we may always deduce therefrom its elec- 

 trical charge under a given greater intensity, since we only require to de- 

 termine the increased quantity requisite to bring the electrometer indica- 

 tion up to the given required intensity. This is readily deduced, the 



