Mr. Wildbore on Spherical Motion. 497 
M. Landen’s very important difcovery, that every body, 
be its form ever fo irregular, will revolve in the fame manner 
as if its mafs were equally divided and placed in the eight 
angles, or difpofed in the eight odlants of a regular parallelo- 
pipedon, whofe moments of inertia round its three permanent 
axes are the fame as thofe of the body, ferves admirably to 
fhorten the inveftigation, and render the folution perfpicuous. 
I have therefore here taken its truth for granted, becaufe it is 
alfo exactly agreeable to the folutions of the other gentlemen, 
and faves the trouble of repeating what they have done before. 
I have alfo (hewn wherein, and why, his folution differs from 
theirs, and proved, as I think, undeniably, in what refpects it 
is defective. * 
That the inertia, or, as M. Euler calls it, the momentum 
of inertia , is equal to the fluent or fum of every particle of the 
body drawn into the fquare of its diftance from the axis of 
motion ; and the determination of the three permanent axes, 
or the demonftration that there are, at leaft, three fuch axes in 
every body, round any one of which, if it revolved, the velo- 
city would be for ever uniform, I have alfo taken for granted, 
, becaufe thefe things have been proved before, and all the gen- 
tlemen are agreed in them. Difficulties that occurred I have 
not concealed, but {hewn how to obviate, and endeavoured to 
place the truth in as clear a light as pofiible ; which to difco- 
ver is my wifh, or to welcome it by whomfoever found. 
proposition 1. 
Whilft a globe, whofe centre is at reft, revolves ■ with a 
given velocity about an axis paffing through that centre, to 
Yol. LXXX. Ttt find 
