the Rotatory Motion oj Bodies^ 



o 



I 



6':> 



that being, by feme force or forces, made to revolve about an 

 axis, paffing through its center of gravity, with a certain an- 

 gular velocity, it fhall move exadly in the fame manner as any 

 other given body will move, if made to revolve, by the fume 

 force or forces, about an axispading 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 dimenlions of a pa- 

 rallelopipedon that fhall be affected exadly in the fame manner 

 as any other given body will be affeded, as well with regard to 

 the centrifugal force of the refpeftive particles of the bodies, as to 

 the adlion of equal percuffive forces, or ofcillation ; it will, 

 after (hewing how the dimenfions of fuch parallelopipedon may 

 be computed, be only neceffary, in inveftigating the proportion 

 under confideration, to determine the tracks and velocities of 

 the poles of the momentary axis, about which any parallelopi" 

 pedon may be made to revolve. 



Firft then to find fuch parallelopipedon (P), that, with re- 

 fpe£l: to the a6lion of fuch forces as are mentioned above, it 

 may be affefted exa£lly in the fame manner as any other given, 

 body (Q). Let it be confidered that G(tab.X.fig.i.) being the 

 centerof gravity, N a point of fufpenfion, and O the correfpond- 

 ing center of ofcillation or percuffion, the redangle GN x GO 

 will be an invariable quantity, the diredlion NGO continuing 

 the fame ; and that a cylindric furface being defcribed, fuch 

 that the center of the middle circular fe6lion thereof fliall be 

 G, and radius —s/Q^ x GO, and whofe axis (hall 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 



