the Rotatory Mot ion of Bodies . ji 5 
that being, by fome force or forces, made to revolve about an 
axis, paffing through its center of gravity, with a certain an- 
gular velocity, it fhall move exactly in the fame manner as any 
other given body will move, if made to revolve, by the lame 
force or forces, about an axis paffing through its center of gra- 
vity; the quantity of matter (as well as the initial angular 
velocity) being fuppofed the fame in both bodies ; and due re- 
gard being had, in the application of the moving force or 
forces, to the correfponding planes in the bodies. Therefore, 
as we may from thence always affign the dimenfions of a pa - 
rallelopipedon that fhall be affected exactly in the fame manner 
as any other given body will be affedled, as well with regard to 
the centrifugal force of the refpedtive particles of the bodies, as to 
the adtion of equal percuffive forces, or ofcillation; it will, 
after fhewing how the dimenlions of fuch parallelopipedon may 
be computed, be only neceffary, in inveftigating the propofition 
under conlideration, to determine the tracks and velocities of 
the poles of the momentary axis, about which any parallelopl - 
pedon may be made to revolve. 
Firff then to find fuch parallelopipedon (P), that, with re- 
fpedl to the adtion of fuch forces as are mentioned above, it 
may be affected exadtly in the fame manner as any other given 
body (Q). Let it be confidered that G (tab.X.fig.i.) being the 
center of gravity, N a point of fufpenfion, and O the correfpond- 
ing center of ofcillation or percuffion, the redtangle GN x GO 
will be an invariable quantity, the diredtion NGO continuing 
the fame ; and that a cylindric furface being defcribed, fuch 
that the center of the middle circular fedtion thereof fhall be 
G, and radius — _ \/ GN x GO, and whofe axis fhall be perpen- 
dicular to the plane wherein the line NGO is fuppofed to be 
impelled to move; if all the matter in the body were placed 
any 
