Green on Cavendish's Electric Theory 367 



"It is almost needless to say the author just alluded to is the celebrated 

 CAVENDISH, who having confined himself to such simple methods as may 

 readily be understood by any one possessed of an elementary knowledge of 

 geometry and fluxions, has rendered his paper accessible to a great number of 

 readers; and although, from subsequent remarks, he appears dissatisfied with 

 an hypothesis which enabled him to draw some important conclusions, it will 

 readily be perceived, on an attentive perusal of his paper, that a trifling altera- 

 tion will suffice to render the whole perfectly legitimate. 



"Little appears to have been effected in the mathematical theory of elec- 

 tricity, except immediate deductions from known formulae, that first presented 

 themselves in researches on the figure of the earth, of which the principal are, 

 the determination of the law of the electric density on the surfaces of con- 

 ducting bodies differing little from a sphere, and on those of ellipsoids, from 

 1771, the date of CAVENDISH'S paper, until about 1812, when M. POISSON pre- 

 sented to the French Institute two memoirs of singular elegance, relative to the 

 distribution of electricity on the surfaces of conducting spheres, previously 

 electrified and put in presence of each other. 



[Footnote.] "In order to make this quite clear, let us select one of Caven- 

 dish's propositions, the twentieth for instance [Art. 71], and examine with some 

 attention the method there employed. The object of this proposition is to show, 

 that when two similar conducting bodies communicate by means of a long 

 slender canal, and are charged with electricity, the respective quantities of 

 redundant fluid contained in them will be proportional to the n i power of 

 their corresponding diameters ; supposing the electric repulsion to vary inversely 

 as the n power of the distance. 



"This is proved by considering the canal as cylindrical, and filled with in- 

 compressible fluid of uniform density: then the quantities of electricity in the 

 interior of the two bodies are determined by a very simple geometrical con- 

 struction, so that the total action exerted on the whole canal by one of them 

 shall exactly balance that arising from the other; and from some remarks in 

 the 27'" proposition [Arts. 94, 95] it appears the results thus obtained agree 

 very well with experiments in which real canals are employed, whether they 

 are straight or crooked, provided, as has since been shown by Coulomb, n is 

 equal to two. The author, however, confesses he is by no means able to de- 

 monstrate this, although, as we shall see immediately, it may very easily be 

 deduced from the propositions contained in this paper. 



"For this purpose let us conceive an incompressible fluid of uniform density, 

 whose particles do not act on each other, but which are subject to the same 

 actions from all the electricity in their vicinity, as real electric fluid of like 

 density would be; then supposing an infinitely thin canal of this hypothetical 

 fluid, whose perpendicular sections are all equal and similar, to pass from a 

 point on the surface of one of the bodies through a portion of its mass, along 

 the interior of the real canal, and through a part of the other body, so as to 

 reach a point A on its surface, and then proceed from A to a in a right line, 



