122 ON THE LAWS OF 



section of a plane perpendicular to the ray Op with the surface 

 of the sphere itself, provided n is greater than 2. When on the 

 contrary n is less than 2, this law requires a certain modification ; 

 the nature of which has been fully investigated in the article just 

 named, and the one immediately following. 



It has before been remarked, that the generality of our ana- 

 lysis will enable us to assign the density of the free fluid which 

 would be induced in a sphere by the action of exterior forces, 

 supposing these forces are given explicitly in functions of the 

 rectangular co-ordinates of the point of space to which they 

 belong. But, as in the particular case in which our formulae 

 admit of an application to natural phenomena, the forces in 

 question arise from electric fluid diffused in the inducing bodies, 

 we have in the ninth article considered more especially the case 

 of a conducting sphere acted upon by the fluid contained in any 

 exterior bodies whatever, and have ultimately been able to 

 exhibit the value of the induced density under a very simple 

 form, whatever the given density of the fluid in these bodies 

 may be. 



The tenth and last article contains an application of the 

 general method to circular planes, from which results, analogous 

 to those formed for spheres in some of the preceding ones, are 

 deduced ; and towards the latter part, a very simple formula is 

 given, which serves to express the value of the density of the 

 free fluid in an infinitely thin plate, supposing it acted upon by 

 other fluid, distributed according to any given law in its own 

 plane. Now it is clear, that if to the general exponent n we 

 assign the particular value 2, all our results will become appli- 

 cable to electrical phenomena. In this way the density of the 

 electric fluid on an infinitely thin circular plate, when under the 

 influence of any electrified bodies whatever, situated in its own 

 plane, will become known. The analytical expression which 

 serves to represent the value of this density, is remarkable for 

 its simplicity ; and by suppressing the term due to the exterior 

 bodies, immediately gives the density of the electric fluid on a 

 circular conducting plate, when quite free from all extraneous 

 action. Fortunately, the manner in which the electric fluid 



