248 Literary and Philosophical Society. 



of a quantity dependent on the continuance of a given 

 vis motrix for a certain time may have its use when cor- 

 rectly applied in certain philosophical considerations, but 

 the idea of the same force exerted through a determinate 

 space is of greater practical utility, as it occurs daily in the 

 usual occupations of men. Wollaston's views closely 

 coincide with those of Smeaton. The Edinburgh Re- 

 viewers, however, on Wollaston's essay, adopt a different 

 doctrine. The opinion of Laplace on the question is quoted, 

 ' La force peut etre exprimee par une infinite de fonctions 

 de la vitesse qui n'impliquent point contradictions, il n'y 

 en a point par exemple a la supposer proportionnelle au 

 carre" de la vitesse/ Laplace thinks the law of inertia and 

 the law of force proportional to the velocity, are the most 

 natural and most simple principles imaginable, that they 

 are derived from the very nature of matter, and that they 

 are the only facts which the science of mechanics borrows 

 from experience. In connection with the measure of 

 moving force reference is made to Smeaton's work on 

 water-wheels. Ewart thinks Smeaton's four maxims on 

 undershot wheels may all be comprehended in one ex- 

 pression, thus : that in cases where the maximum effect is 

 produced it is nearly as the quantity of water multiplied 

 by the effective head. Ewart refers to some experiments 

 of Bossut on water-wheels, giving results agreeing very 

 nearly with Smeaton's conclusions. Borda and Waring 

 attempted to show that the force of the water against the 

 wheel is not proportional to the square of the velocity 

 with which it strikes the wheel, but that it is in the simple 

 ratio of that velocity. Ewart objects to Waring's demon- 

 stration, leading he thinks to the conclusion that we may 

 double the power of any undershot wheel (whatever may 



