Of GREATEST ATTRACTION. 243 



BG a = EC 1 , therefore c - EC or BD. So alfo, c* -f a = 

 BD* + BA* =s AD', beeaufe ABD is a right angle, &c. Thus, 



F'---.*-.V4-BE L.o~ (AF + FN)AE 

 F-^-^+B^.Log (AD + DE) (AN + 



(AF + FM) AC 

 B^-^S (AD + DC) AM* 



This expreflion for the attraction of a parallelepiped, though 

 confiderably complex, is fymmetrical in fo remarkable a de- 

 gree, that it will probably be found much more manageable, 

 in inveftigation, than might at firft be fuppofed. That it mould 

 be fomewhat complex, was to be expected, as the want of con- 

 tinuity in the furface by which a folid is bounded, cannot but 

 introduce a great variety of relations into the expreflion of its 

 attractive force. The farther Amplification, however, of this 

 theorem, and the application of it to other problems, are 

 fubjects on which the limits of the prefent paper will not 

 permit us to enter. The determinations of certain maxima de- 

 pend on it, fimilar to thofe already inveftigated. It points at 

 the method of finding the figure, which a fluid, whether elaftic 

 or unelaftic, would afliime, if it furrounded a cubical or prifma- 

 tic body by which it was attracted. It gives fome hopes of be- 

 ing able to determine generally the attraction of folids bound- 

 ed by any planes whatever ', fo that it may, fome time or other, 

 be of ufe in the Theory of Chryflallization, if, indeed, that 

 -theory fhall ever be placed on its true bafis, and founded, not 

 on an hypothefis purely Geometrical, or in fome meafure arbi- 

 trary, but on the known Principles of Dynamicks. 



Vol. VI.— P. II. Hh V. 



