432 M. Poinsot on the Percussion of Bodies. 
6. We have now to find the velocity of the particular point C 
under the influence of these forces and couples. 
7. In the first place, the three forces applied to the centre of 
gravity impart to every point of the body, and therefore to C, 
the velocities Ke kia saa eam Z (1) 
mi? mm Past ihe 
along the coordinate axes of a, y, 2 respectively. 
8. In the second place, the three couples tend to cause the 
body to turn around these axes with angular velocities whose 
respective values are 
L,+Zy—Yz M,+ X2—Ze No+Ya—Xy 
PAT gems td ee 2= m/s? pi eS Baw (2) 
But it will easily be seen that, in virtue of these three rota- 
tions, the point C will have, in the directions of the axes of 
2, y, 2, the velocities 
qz—Ty, Tr2@—pz, py-qe .. . . (8) 
respectively. Consequently, by adding these velocities to the 
three preceding ones, and representing by 2, y, z the total velo- 
cities of the point C along the coordinate axes of 2, y, 2, we shall 
have Ki4-% 
m 
Ly 
m 
2= 
+92—"y, 
i +rx—pz, 
ee re 
Sie Sie apie, pak: 
whence, by substituting the values of p, g, 7 as given in (2), we 
deduce the three equations 
ati X,+X = 2(M)+X2—Zz)  y(No>+Yx—Xy) 1 
m mB? my” 
j= YotY¥ , a(Not¥e—Xy) _ 2(lp+Zy—-¥e) |, (a) 
cae my? maz 
Zo+ Z y(Lo+ Zy— Yz) «(Mo+ Xz—Za) 
ga Ty Wor | 
m ma mp 
9. These are the equations which furnish at once the compo- 
nents 2, i/, 2 of the velocity 7 imparted to the point C of the body 
by the given forces which animate the same, combined with the 
unknown force —Q supposed to be applied at the point C itself. 
10. But the foree —Q being properly chosen, the velocity 7 
of the point C, and consequently each of the components 2, y, ~ 
of this velocity will become zero. 
Putting z=0, y=0, 2=0, therefore, the formule (A) give 
