4 Mr green, on THE LAWS OF THE EQUILIBRIUM OF FLUIDS. 



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 fol- 

 lowing. 



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

 ducting 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, analagous 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 ex- 

 ponent 11 we assign the particular value 2, all our results will become 

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

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

 fluence of any electrified bodies whatever, situated in its own plane, 

 will become known. The analytical expression which serves to repre- 

 sent the value of this density, is remai-kable 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 distributes itself in the latter case, has long since 

 been determined experimentally by Coulomb. We have thus had the 

 advantage of comparing our theoretical results with those of a very 



