62 Mr green, ON THE LAWS OF THE EQUILIBRIUM OF FLUIDS. 



We thus see that the differences between the calculated and observed 

 densities are trifling; and moreover, that the observed are all something 

 smaller than the calculated ones, which it is evident ought to be the 

 case, since the latter have been determined by considering the thickness 

 of the plate as infinitely small, and consequently they will be somewhat 

 greater than when this thickness is a finite quantity, as it necessarily 

 was in Coulomb's experiments. 



It has already been remarked that the method given in the second 

 article is applicable to any ellipsoid whatever, whose axes are a, h, c. 

 In fact, if we suppose that x, y, % are the co-ordinates of a point p 

 within it, and x', y', z' those of any element dv of its volume, and 

 afterwards make 



X = a. cos 9, y — i.sin 6 cos w, a = c.sin 6 sin ■sr, 

 x'= a. cos ff, y' = J. sin 9' cos w', z'= c.sin 9' sin w', 

 we shall readily obtain by substitution. 



l-n 

 2 . 



■ V=abcf p. r'^dr'd&d-ar' si-n 9'. {Xr"- 2 nrr'-¥vr'^) 

 the limits of the integrals being the same as before (Art. 2.), and 

 \ = «^ cos 9^ + If sin 9^ cos ts^ -\- & sin 0- sin Tsr^, 



ft. = a^ cos 9 cos 9' + U sin 9 sin 9' cos tb- cos in-' ■\-<? sin 9 sin 9' sin •ar sin w', 

 V = «' COS 9" + ¥ sin 9'^ cos sr'^ + e sin 9'^ sin ■ar'^ 



