MOVING FORCB, 
245 
gravity ; and that, in cases of composition of motion, where- Cnses of diffi- 
ever there is a loss of mechanical force in any direction, there of 
must be a corresponding change of figure, which may always moving force, 
be estimated upon the principles adopted in the preceding cases. 
In the 10th case, the quantity of motion of A (fig. lO) after 
collision, is the same as that of the common centre of gravity of 
E and F before collision. But the whole forces of E and F are not 
exhibited in the quantity of motion of their common centre of 
gravity. The motion of A, however, is the whole effect pro- 
duced, and if we estimate its force by its mass into its velocity, 
W'C cannot account for the tot.al loss of the forces of E and F ; 
but if we estimate all the forces by the masses into the squares 
of their separate velocities, the .agreement between the forces 
and their joint effect is obvious. ‘ 
I have alrc.idy adverted (page 134) to a statement of a case 
of composition of motion made by M. I.jplace, in which a 
hypothetical relation of the force of a body in motion to the 
square of its velocity is adopted, ami where the supposed effects 
would be quite at variance with those of experience. It will, 
perhaps, bef^etter uwlerstood with a reference to this lOth case. 
M. LapKic© says, “ La force pent etre exprim6e par one 
iniintt6 de» fonctions de la vifesse, qui n’ impliquent pas contra- 
diction. II n'y en a point, par exemple, a la snpproser prepor- 
I tionrelle an c.'irr6 de la vipesse. Dans cette hyjrothdw, il cst 
facile dc determiner )e mouvement d’nn point solicite par un 
nombre quelconque de forces, dont les vitesses sent conn ties ; 
I car si Ton prend sur les directions de ces forces, ^ partir de lenr 
' point d« coocurs, de droites pour representer leurs vitesses, fet 
I ki Ton determine sur ce memes directions, en parrant du mftme 
point, de nouvelles droites qui soient entreellcs, coromes les 
I carres des premieres ; ces droites pourront reprfisenter les forces 
leUe-mSmes. En les composant ensnite par ce qui precede, on 
.aura la direction do la n'isultante, ainsi que la droite qui Tex-- 
prime, et qui sera an carre de la vitesse correspondante, comme 
la droite qui represente une des forces composantes, est au carre 
)«« sa vitesse. On volt par D, comment on pe«t determiner le 
ZDouvement 
