134 On the Measure of 
remarks on supposed errors of Mr. Smeaton, — 
which I shall have occasion to refer to again, 
they say, “ 'T'o whatever cause, therefore, the 
imperfection of the theory of the machines 
moved by water is to be ascribed, it is not to 
any thing that would be corrected by the 
introduction of a measure of force different 
from that which is commonly in use.”* At 
the beginning, however, of the same article, | 
they give the following opinion: “It is no 
longer doubted that this force (of percussion) 
may, with perfect truth, be considered as 
proportional, either to the quantity of matter 
multiplied into the velocity, or to the quantity 
of matter multiplied into the square of the 
velocity, according to the nature of the effect 
which it is destined to produce.” + 
On the subject of forces, M. Laplace ex- 
presses. himself as follows: “La force peut 
étre exprimée par une infinité de fonctions de 
la vitesse, qui n’impliquent point contradiction. 
Iln’y en a point, par exemple, a la supposer 
proportionnelle au carré de la vitesse.” t After 
stating a hypothetical example of force, where 
the results would be different from those of 
experience, but where the square of the velo- 
* Edin. Rev. vol. 12, p. 126. + Ibid. p. 120. 
£ Systeme du Monde, 3d edit. Livy. III. ch. 2, p. 141. 
