t6 Review of O. Gregory'' s Treatise on Mechanics. 



If F be put for the force, M the mass, or number of parti- 

 cles in a body, and V it? velocity, then is F aM V, and 

 V cc ^. If V be constant, then is F proportional to M, the 

 mass; but why is it so, unless it be by the inertia, or the 

 greater force of a greater mass r If M be indefinitely small, 

 and F be constant, then is V indefinitely great, or if the 

 mass or inertia be nothinfj, the velocity would be indefinite- 

 ly great, so that if there were not in matter a force of iner- 

 tia proportional to its mass, the least force would cause a 

 body on which it acts, to move with an infinite velocity ; 

 but that it is not infinite, and that the velocity is modified to 

 a definite quantity in the inverse ratio of the mass, is wholly 

 the effect of the force of inertia. 



After delivering Newton's three laws of motion, the au- 

 thor goes into long arguments a priori, and a posteriori, to 

 prove their validity. Now nothing can be more obvious, 

 evident, and undeniable than those laws, if we except that 

 of a body in motion continuing in motion, unless some force 

 or power obstruct it. This is sufficiently proved by one 

 decisive experiment of Newton, viz. that the destruction of 

 motion is precisely commensurate with the obstructing 

 cause and >ts proper effect. When therefore there is no ob- 

 structing cause, there is no diminution of motion, or it remains 

 constant. The remarks of the author on this subject are an 

 instance of the unnecessary and extreme diffusion in some 

 parts of his work, when compared with the neatness and 

 conciseness of others. In chapter 2d. Art. 36, a funda- 

 mental principle is advanced, that the result-ant of two equal 

 forces, acting at a point, bisects the angle, which the direc- 

 tions of the forces make with one another. No proof is 

 given of this, but the Leibnitzean, and metaphysical one of 

 the suflicient reason. It ought either to be proved directly, 

 or by the reductio ad absurdum, or assumed as an axiom, 

 or intuitive truth, not susceptible of demonstration. The 

 same objection lies against another fundamental proposition, 

 in Art. 38, which is not attempted to be proved, though it 

 is made the basis of the succeeding proposition, intended 

 to demonstrate the parallelogram of forces. 



This demonstration, if it may so be called, appears to be 

 compounded, of what had been done by D'Alembert and 

 otliers, by the analytical and far-fetched method of the 

 moderns, which, however valuable in itself, is certainly de- 



