Rotatory Motion of Bodies. 19 
Let m+tm = G; m’ +m = B, m +m! = A*; 
-m—m = B— A, m—m'=C—B, m'—m=A-C; 
(k), 
which are the equations of Eulert. And hence it appears, that 
in this cdése the equations coincide with those which are always 
given for the motion of a solid body by foreign Mathematicians, 
and differ from the results which Mr. Landen obtained by his 
method. 
“. Cdr +(B- A)pqdt 
Adp + (C — B) qrdt 
Bdq+(4-C)prdt 
ll 
oo 0 
ll 
The equations above obtained agree with the general equa- 
tions for the motion of any solid body of which A, B, C, are the 
moments of inertia with respect to the three principal axes. 
Hence it appears, that whatever the body be which revolves 
about a given centre, we may always take a system consisting 
of three material points, such, that their motion shall be exactly 
- similar to that of the body. Mr. Landen had observed, that it 
is always possible to substitute for a solid body a system of 
eight material points placed at the angles of a parallelepiped, 
whose centre is the centre of motion; but I am not aware of 
its having been noticed, that these may be replaced by three 
points. If we wished, in our system of points, to have their 
centre of gravity coincident with the centre of motion, we may 
conceive each of the lines mO, m0, m'O" to be produced, and 
an equal distance and an equal point to be taken on the oppo- 
Se ea eee ee 
* It is manifest that m4+-m’ or C is the moment of the system round the axis Om’; 
and similarly, B and A are the moments round Om and Om. 
+ Euler, Theoria Motus Corp. Rig. Prop. 90. Poisson, Dynamique, Art. 383. 
c2 
