246 
MOVING FORCE. 
I- 
Cases of diffi- mouvement, d’un pointj quelle que soil la fonction de la vi- 
clocf,.’ les of P 
moving force. Now, If AB (fig. lOtb) be produced to G, and AC to H, 
r 
% 
making AH : AC® : : AG : AB®, and if we complete the rec- ,, 
tangle, and draw the diagonal AI, we shall have a diagram of ^ 
the construction described above by M. Laplace ; and, if I ,i 
understand him right, he concludes, that if the forces of E 
and F are respectively as the squares of their velocities, AI 
must be the resulting direction of A, and the square of its ^ 
vJocity must be to AI as AB® • AG. If, by the force of a 
body in motion, being as the square of its velocity, it were 
• • • ^ 
meant, that the pressure exerted in bringing it to rest in a ^ 
given time, must be as the square of its velocity, the result _ ^ 
must, no doubt, be such as M. Laplace describes. I cannot ^ 
find, however, that this meaning has ever been applied to the 
principle in question. Such a hypothesis could not be enter- 
tained, indeed, fora moment, without setting aside the incon- 
trovertible explanations and conclusions of Galileo. In answer 
.0 ihe objccllon implW/m ,he reasoning ofM. Laplace, against . J 
the force being as the square of the velocity, I can only repeat 
what 1 have already so often repeated, that it is not the pres- ^ 
sure exerted in a given time, but the pressure exerted through 
a given space, that is understood to be universally as the mass 
into the square of its velocity j and I may add that there i« 
nothing hypothetical in this conclusion. Being derived from, 
an induction of facts, it must stand or fall with the facts on 
. I 
which it Is grounded. 
In the next case, where the angle BAG (fig. 1 1) is riot a 
right angle, the results after collision are, in two respects, dif- ^ 
ferent from the last. E and F are not at rest after collision, . J 
and the quantity of motitji of A is not the same as that of the 
common centre of gravity of E and F before collisionf. This 
.. 
• Systeme du Monde, p. 141 . 
+ In describing this case at page 123, I Lave omitted to state, that 
K and P are supposed to move with equal velocities; but it will be 
obvious, from the figure, and from the results which are given, that it 
was so understood. 
case. 
