Spherical Motion . 5 r y 
great circles be found, in the fame manner as in the particular 
cafe here ipecified. And it will alfo be found for any pofition 
of O, by means of the expreffions for the velocities found in 
Scholium I. Prop. iv. ; but of this more hereafter. 
PROPOSITION VI. 
If a parallelopipedon (or other * folid) revolving uniformly 
with an angular velocity =# about one of its permanent axes 
of rotation, receive an inftantaneous impulfe in a diredlion pa- 
rallel to that axis, the centre of gravity of the body being 
fuppoied to be kept at reft by an equal and contrary impulfe 
given to it, and no other force adting upon the body, it is. 
propofed to determine the alteration in the motion thereof,, 
in confequence of fuch inftantaneous impulfe. 
The impulfe being, by hypothefis, given in a diredlion per- 
pendicular to that of the then only motion of every particle of 
the body, cannot inftantly alter its angular velocity about the 
permanent axis ; but its immediate effedt muft be to caule the 
body to revolve about a frefh axis, whilft the angular velocity, 
and confequently the momentum of rotation about the firft or 
permanent axis, remain unaltered by fuch inftantaneous im- 
pulfe; for though it gives a different diredlion and velocity to 
the particles, by caufing them to revolve about another axis, 
yet muft their relative velocity about the firft remain unaltered 
by the nature of relative motion, becaufe the fecond or addi- 
tional motion is given in a diredlion perpendicular to the firft.. 
Any alteration therefore which may be made in the velocity 
about the firft axis, by reafon of the oblique motion of the 
particles about it, owing to the then revolution about a frefh 
axis, muft be a work of time. And to determine fuch alteration, 
% See the note (Cf at the end of the Paper, 
let 
