/ 
the Rotatory Motion of Bodies. 317 
Whence we may infer, that the parallelopipedon (P N , which 
we propofed to find, mud; have the dimen ficus laid written ; 
namely, length, breadth, and thicknefs, refpedively equal to 
s/bd 2 + pj 2 - 6e~, \/6e* + 6J* - 6d\ and s/bd* + 0e z - 6J z : 
which may be confirmed by a more drift demondration founded 
on the principles made life of in my fourth Memoir. For it 
appears by what is there proved, that the centrifugal forces of 
the particles of any revolving body, in two directions at right 
angles to each other, may be expreded in terms of A, B, K, 
and variable quantities {hewing the pofition of the momentary 
axis ; and that, in a parallelopipedon whofe dimenfions (length, 
breadth, and thicknefs) are a, h, k ; and whofe mafs, or con- 
tent* is = M; A will her- — , B — — , andK= — . If there- 
’ 12 12 12 
fore a be = f6d z + 6/' 2 — 6e\ b = f be z + 6/ 2 - 6dy and k — 
%/6d z + 6 P - 6 /" ; in fuch body, 
A will be = x d~ +j z — e'% 
M 
B =T x ^t j % -d\ 
M — — — -» 
K =— x d~ + er — t a . 
2 J 
But, in any body whatever, 
M x d 1 is = the fum of all the + z z x p, 
Mxf« = the fum of all thejy 2 + sd x p 9 
M xf z — the fum of all the.xf+y xp, 
and — x d 1 - + e z + j % — the fum of all the x l +y* + z 1 x p : x 9 y, 
and % correfponding to the place of the particle p in the body ; 
x being meafured from the center of gravity upon a permanent 
axis of rotation, y at right angles to x 9 and z at right angles 
to 
