2 1 6 Mr . L an den’s Invejligation of 
any where in that furface, fo that G fiiould be the center of 
gravity of the matter fo placed, any given force or forces, a&ing 
on the body in the plane juft now mentioned, would caufe the 
line NGO in the body to move exactly in the fame manner as it 
would move, if it were carried with the matter placed in the 
laid fur face (as before-mentioned) after having been put in 
motion by the action of the fame force or forces. Moreover, 
let it be confdered, that there will at leaf; be three permanent 
axes of rotation in the body Q, at right angles to each other 
(as I have proved in my Mathematical Memoirs ) ; and that, 
fuppofmg NGO to coincide with thofe three axes in three fuc- 
ceffive cafes wherein the' matter in QJhall, in each cafe, be con- 
ceived to be placed in a cylindric furface as delcribed above, we 
may conceive it pofiible fo to place the matter of , the body, 
that all of it (hall be in each of thofe three fur faces, and G 
ftiil continue its center of gravity. And, a computation being 
made accordingly, it appears, that the matter of the body Q 
muft be placed, in equal quantities, at each of the eight an- 
gular points of a p ar a lied o pipe don (R) whofe dimenfions 
(length, breadth, and thicknels) frail be s/ zd z + zf 1 - ze\ 
v/ 2 f + 2 / J - £d\ and Mzd 2 + ze r - 2 / 2 ; d, e, and f being 
the three values of s/Gdl x GO, when NGO is fucceffively a 
permanent axis of rotation, with refped to the body Q, in 
three directions at right angles to each other. 
If Q^were a parallelopipedon, it may be eafily proved, 
that its dimenfions muft be v 7 bd~ + 6/ " - 6<r, v 7 be + 6/ 1 — 6a\ 
and s/h d z + be 2 - 6/% that the correlponding parallelopipedon, 
at the angular points whereof the matter of Q is conceived to 
be placed as above, may have the fame dimenfions as thofe 
which we have found our parallelopipedon R muft have. 
2 Whence 
