53 ° 
Mr. Wildbore on 
proposition VII. 
If a body of any form revolve in any manner whatfoever 
with its centre of gravity at reft in absolute fpace, and to as 
not to be difturbed by the aftion of any external force; to 
determine in what manner it will continue its motion for 
ever. 
Since any body whatever, whofe permanent axes can be 
found, may be reduced to an equipollent parallelopipedon which 
lhall move in the very fame manner as the body ; let this be 
fuppofed done, M being the mafs or folidity of the body, and 
Mu', M b~, and Mc% the refpedtive momenta of inertia round 
the three permanent axes of the body whofe poles in the fpheri- 
cal furface whofe radius is unity revolving as the body revolves 
and concentric with it are A, B, andC, at thediftanceof a qua- 
drant from each other (fig. 8.); let x = the velocity with which 
the body moves round the permanent axis whole pole is A, 
and meafured along the great circle BC at the diftance of a 
quadrant from that pole (A) and in the fenfe from B towards 
C ; in like manner, let y = the velocity round the axis whofe 
pole is B, meafured along CA, and in the fenfe from C towards 
A, and 2, = that round the remaining permanent axis whofe 
pole is C meafured along AB, and in the fenfe from A towards 
B. Allb let * = the time from the commencement of the 
motion 
DtlOll® 
Then, the quantities which in the 6th Proportion were repre 
fented by £ *7+7, j xW, j * 
d —ZL , and c -~^ t refpedtively 
a 2 +A’ d 2 + t> 2 ’ <*+» r 
mui 
