Comparison of similar bodies 53 



close to the surface, which will either be as full of fluid as it can hold, or 



will be entirely deprived of fluid; but it will be disposed as nearly in a 



similar manner in both, as is possible. To explain this, let BDE and bde 



(Fig. n) be the two similar bodies; and let the 



space comprehended between the surfaces 



BDE and FGH (or the space BF as I shall call 



it for shortness) be that part of BDE, which 



is either as full of fluid a- it can hold, or 



entirely deprived of it : draw the surface fgh, 



such that the space bf shall be to the space 



BF, as the quantity of redundant or deficient 



fluid in bde, to that in BDE, and that the Fig. n. 



thickness of the space bf shall everywhere bear 



the same proportion to the corresponding thickness of BF : then will the 



space bf be either as full of fluid as it can hold, or entirely deprived of it ; 



and the fluid within the space fgh will be disposed very nearly similarly 



to that in the space FGH. 



For it is plain, that if the fluid could be disposed accurately in a 

 similar manner in both bodies, the fluid would be in equilibrio in one 

 body, if it was in the other : therefore draw the surface /?Se, such that the 

 thickness of the space /?/ shall be everywhere to the corresponding thick- 

 ness of BF, as the diameter of bde to the diameter of BDE; and let the 

 redundant fluid or matter in bf be spread uniformly over the space fif; 

 then if the fluid in the space fgh is disposed exactly similarly to that in 

 FGH, it will be in equilibrio; as the fluid will then be disposed exactly 

 similarly in the spaces /JSe and BDE: but as by the supposition, the 

 thickness of the space /?/ is very small in respect of the diameter of bde, 

 the fluid or matter in the space bf will exert very nearly the same force 

 on the rest of the fluid, whether it is spread over the space J3f, or whether 

 it is collected in bf. 



68] PROP. XVIII. Let two bodies, B and b, be connected to each 

 other by a canal of any kind, and be either over or undercharged: it is 

 plain that the quantity of redundant or deficient fluid in B, would bear 

 exactly the same proportion to that in b, whatever sort of matter B con- 

 sisted of, if it was possible for the redundant or deficient fluid in any body 

 to be disposed accurately in the same manner, whatever sort of matter 

 it consisted of. For suppose B to consist of any sort of matter; and let 

 the fluid in the canal and two bodies be in equilibrio: let now B be made 

 to consist of some other sort of matter, which requires a different quantity 

 of fluid to saturate it ; but let the quantity and disposition of the redundant 

 or deficient fluid in it remain the same as before : it is plain that the fluid 

 will still be in equilibrio; as the attraction or repulsion of any body 

 depends only on the quantity and disposition of the redundant and 



