ELECTRICAL DENSITY. 



According to Franklin, a -body in the natural state contains a 

 normal quantity of the electrical fluid, and it becomes positively or 

 negatively electrified, according as its charge of fluid is increased or 

 diminished by the action of external bodies. The attractions and 

 repulsions of bodies are explained by the mutual repulsion of the 

 fluids, and by the attraction which they exert upon ponderable 

 masses. 



The hypothesis of two fluids, devised by Symmer, and adopted, 

 at any rate provisionally, by Coulomb, assumes that there are two 

 different fluids, that the molecules of the same fluid repel, and that 

 different fluids attract; and, finally, that in a body in the natural 

 state, there are equivalent quantities of the two fluids forming the 

 neutral fluid. A body is electrified positively or negatively, according 

 as it contains an excess of one or the other fluid. Attractions and 

 repulsions are explained in like manner by the actions which they 

 exert between the fluids and the ponderable matter. 



It is the least defect of these hypotheses that they are superfluous. 

 As, moreover, experiment indicates no limit to the electrification of 

 a body, we are led to the conclusion that the normal charge of a 

 body on Franklin's theory, or that the mass of neutral fluid in the 

 theory of two fluids, is unlimited a conclusion that is manifestly in 

 contradiction with the notion of a material, fluid. 



A certain number of expressions used in the study of electricity 

 have originated in the idea of fluids ; there is no inconvenience in 

 retaining them, if we are careful to define them by the mathematical 

 and experimental properties to which they correspond, with the 

 object, as Coulomb expressed it, " of presenting the results of calcu- 

 lation and of experiment with the fewest elements possible, and not 

 of indicating the true causes of electricity."* 



18. ELECTRICAL DENSITY. The idea of a fluid has thus led to 

 that of electrical density. If the electricity occupies the whole 

 extent of a body, in the case of a dielectric for instance, and that it 

 is distributed uniformly, electrical density is the quantity of electricity, 

 defined as above, which exists in the unit of volume. If the distri- 

 bution is irregular, the density at a point is the ratio of the electrical 

 charge of an element of volume at the point to that of the volume 

 itself. 



Conductors only possess electricity on the surface. If the distri- 

 bution is uniform, the superficial density is the quantity of electricity 

 which exists upon the unit of surface. In the case of any given 



* Histoire de V Academic des Sciences pour 1788, p. 673. 



