iJye Rotatory Motion of Bodies, ^ i y 



Whence we may infer, that tl\e parallcloplpedon {P\ which 

 we propoi'ed to find, muft have the dimenficns laft written ; 

 namely, length, breadth, and thicknefs, refpedively equal to 

 ^6d^- + 0/ ' - 6r, s/"6? -{-bj^ -(yd , and v/6i/- + 0f -6/': 

 which may be connrmed by a iTiore ftri<£t dcmonftration founded 

 on the principles made ufe of in my fourth Memoir, Yov it 

 appears by what is there proved, that the centrifugal forces of 

 fhe particles of any revolving body, in two diredions at right 

 fingles to each other, may be exprefled in terms of A, B, K, 

 and variable quantities fhewing the politlon of the momentary 

 axis ; and tliat, in a parallcloplpedon whofe dimenlions (length, 

 breadth, and thicknefs) are a^ b^ k\ and whofe mafs, or con- 



tent, is — M; A will be~ — , Bn — , andK=— . If there- 

 fore a be — s/bd"- + 6/' - te\ b — \/t)e"^bJ~'-()d'^ and k-=z 

 i/bd' + ti' -bf ; in fuch body, 



A will be = ^ x ^M7^^% 



M 





!■ K =--xd~-\-e'-t\ 



Bat, in any body whatever, 



M >^ .^'is =: the fum of all the IF+z^ xp, 

 Mx e^ = the funi of all they + 2' x p, 

 JV^ xf^ :. •=- the fum of all the x^+y x /, 



and ^— X d' +e"^f" = the fum of all the x'-\-y- + z" xp : x, y, 



2 



and % carrefpondlng to the place of the particle p in the body ; 

 .T being meafured from the center of gravity upon a permanent 

 axis of rotatipn, y at right angles to .v, and z at right angles 



to 



