742 PHILOSOPHICAL TRANSACTIONS. [aNNO 1790. 



towards a = Z», and of ab from a towards b =. c. If these 3 velocities a, bj 

 and c, be constant, the spherical surface will always revolve uniformly about the 

 same axis of the sphere at rest in absolute space. 



Prop. 4. If a spherical surface, whose centre is at rest, revolve in any manner 

 whatever, so that the velocities along the 3 quadrants bounding any octant of 

 it be expressed by any 3 variable quantities oc, y, and z ; to find the necessarily 

 corresponding accelerating forces with which the place of the natural or mo- 

 mentary axis, and the angular velocity of the surface round it, are varied. — ^After 

 the investigation, Mr. W. adds : the preceding general properties of motion ob- 

 tain in all bodies revolving round a centre at rest, be their motion ever so 

 irregular ; the 3 great circles bounding an octant of the spherical surface revolv- 

 ing with the body are also taken ad libitum, being any such circles whatever on 

 the surface ; and hence the following very important consequence is drawn, viz. 

 If any body be in motion, or put in motion, by instantaneous impulse or other- 

 wise, about its centre of gravity at rest in absolute space ; if, by any means, the 

 accelerating forces acting along the 3 great circles bounding any octant of a 

 spherical surface that has the same centre of gravity and revolves with the body, 

 can be found, those acting at every other point of such surface will necessarily 

 follow as natural consequences of these 3, and thus all the motions of such body 

 will be absolutely determined. ' 



Prop. 5. The same being given, as in the last proposition, it is proposed to 

 illustrate the manner in which the surface moves with respect to a point at rest 

 in absolute space. 



Prop. 6. If a parallelopipedon, or other solid, revolving uniformly with an 

 angular velocity = z about one of its permanent axes of rotation, receive an in- 

 stantaneous impulse in a direction parallel to that axis, the centre of gravity of 

 the body being supposed to be kept at rest by an equal and contrary impulse 

 given to it, and no other force acting on the body ; it is proposed to determine 

 the alteration in its motion, in consequence of such instantaneous impulse. 



Prop. 7^ If a body of any form revolve in any manner whatever with its centre 

 of gravity at rest in absolute space, and so as not to be disturbed by the action 

 of any external force ; to determine in what manner it will continue its motion 

 for ever.. 



We have omitted the analytical solutions of these propositions, both because 

 they are not every where exempt from errors, and because various other solu- 

 tions of the general problem are to be found as well in these Transactions as 

 elsewhere, 



XXV. On the Chronology of the Hindoos. By Wm. Marsden, Esq., F. R. S., 



and A. S. p. 56o. 

 Unfortunately for the gratification of rational curiosity, history seems to have 



