. 
gi8 Mr, L AN dev’s Invejligation of 
to y in a plans to which the faid axis is perpendicular. 
Therefore, 
M 
A, which is — the fum of all the a; 1 x p , will be = — x d L -\-j 2 - <?% 
B, —the fum of all the y’xp, z=z~ x d +p z — d z , 
K, “the fum of all the z* x p, — ~ x d z + e z ~ J\ 
Hence it is evident, that d, <?, and f being determined from 
any body whatever, the values of A, B, and K will be the 
fame in that body as in our parallelopipedon P ; and that the 
centrifugal forces of the particles will be the fame in both bo- 
dies. Confequently, their motions about fucceffive momentary 
axes (whofe poles are varied by the perturbation arifing from 
thofe forces), will be the fame in both bodies; their initial an- 
gular velocities being the fame ; as well as the pofition of their 
initial momentary axes, with refpedt to the correfpondent per- 
manent axes of rotation in each body. 
Let us now proceed to find how any parallelopipedon will 
revolve about fucceffive momentary axes palling through its 
center of gravity : by which means, with the help of the 
theorem juft now inveftigated, we fhall be enabled to define 
how any body whatever will revolve about fuch axes ; which is 
the chief purpofe of this difquifition. 
Fig. 2. and 3. The length, breadth, and thicknefs of the 
revolving parallelopipedon (P) being 2 d, 2 c, and 2b, conceive a 
fpherical furface without matter, whofe center is the center of 
gravity of the body P, to be carried about with that body 
during its motion ; and let the faid furface be orthographically 
projected, fo that the radius upon which b is meafured may be 
reprefented 
