66 Royal Society : — * 



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 rectangle 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 exten- 

 sion 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 grouping 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 extension 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 of the 

 surface multiplied into the square root of the boundary. Thus, calling 

 C the charge, S the surface, B the boundary, and fx some arbitrary 

 constant depending on the electrical unit of charge, we have 

 C=^VS.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 boundary, 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 sur- 

 faces 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 /x V 2lb (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 multiplied into the sur- 

 face. If the surface be constant, the intensity is inversely as the 

 boundary. If the boundary 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 electrical charge 

 under a given greater intensity, since we only require to determine 

 the increased quantity requisite to bring the electrometer indication 

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

 intensity being, by a well-established law of electrical force, as the 

 square of the quantity. 



8. These laws relating to charge, surface, intensity, &c, apply 

 more especially to continuous surfaces taken as a whole, and not 

 to surfaces divided into separated parts. The author illustrates this 

 by examining the result of an electrical accumulation upon a plane 



