51 8 Mr,LA}^DE\*s Inv^JigaiiGH of 



to y In a plane to which the fald axis is perpendicular. 



Therefore, 



A, which 15 := the Turn of all the .v* x /», will be = — x ^- +y " - e\ 



M 



B, =:thefumofallthe>'' x^, =:— x e'-" +/ ^ - J\ 



M 



K, =thefumof allthez' X j5, —— x d^ + e' ~J^^ 



Hence it is evident, that cl, e, and^ 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 fucceflive momentary 

 axes (whofe poles are varied by the perturbation arifmg froni 

 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 refpe£l to the correlpondent per^ 

 manent axes of rotation in each body. 



Let us now proceed to find how any parallelopipedon will 

 revolve about fucceflive momentary axes pafling through its 

 center of gravity : by which means, with the help of tb& 

 theorem juft now inveftigated, we fhali be enabled to define 

 how any body whatever will revolve about fuch axes ; which is 

 the chief purpofe of this difqulfition. 



Fig. 2. and 3. The length, breadth, and thicknefs of the 

 revolving parallelopipedon (P) being id, 2c, and 2^, 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 orthographlcally 

 projedled, fo that the radius upon which 5 is meafured may be 



rep re fen ted 



