Of GREATEST ATTRACTION. 237 



This proportion may be proved to be rigoroufly true, if we 

 confider the inverfe ratio of the fquares of the diftances, as a 

 limit to which the other ratio conftantly converges. 



It is a proportion alfo ufually laid down in optics, where 

 the visible space fubtended by a furface, is the fame with what 

 we have here called the angular space fubtended by it, or the 

 portion of a fpherical fuperficies that would be cut off by a 

 line palling through the centre of the fphere, and revolving 

 round the boundary of the figure. The centre of the fphere is 

 fuppofed to coincide with the eye of the obferver, or with the 

 place of the particle attracted, and its radius is fuppofed to be 

 unity. 



The propofitions that have been juft now demonflrated con-* 

 cerning the attraction of a thin plate contained between paral- 

 lel planes, have an immediate application to fuch inquiries 

 concerning the attraction of bodies, as were lately made by Mr 

 Cavendish. 



In fome of the experiments inflituted by that ingenious and 

 profound philofopher, it became neceflary to determine the at- 

 traction of the fides of a wooden cafe, of the form of a parallel - 

 epiped, on a body placed anywhere within it. (Philofophical 

 Tranfactions, 1798, p. 523.). The attraction in the direction 

 perpendicular to the fide, was what occafioned the greater! dif- 

 ficulty, and Mr Cavendish had recourfe to two infinite feries, 

 in order to determine the quantity of that attraction. The de- 

 termination of it, from the preceding theorems, is eafier and 

 more accurate. 



Let MD' (Fig. 15.) reprefent a thin rectangular plate, A, a 

 particle attracted by it, AB a perpendicular on the plane MD', 

 NBC, LBL', two lines drawn through B parallel to the fides of 

 the rectangle MD'. Let AC, AL, AN, AL', be drawn. 



G g 2 , Then, 



