Review of O, Gregory'^ & Treatise on Mechanics. 75 



investigation. The whole subject of the reduction of for- 

 ces to rectangular co-ordinates, and the formulas dependant 

 on it, is only a simple corollary from Newton's laws of mo- 

 tion ; and all that is said of parallel forces is but a corollary 

 of oblique forces acting at a point. 



. In the preliminary remarks, the author says that vis iner- 

 tia is improperly called a force, " because if it were a force 

 it would be of some definite quantity in a given body, and 

 an impressed force less than that would not move the body; 

 whereas any impressed force, however small, will move 

 any body, however great," Force had been previously 

 defined to be " that which causes any change in the state 

 of a body, whether that state be motion or rest." In the 

 collision of bodies, there is necessarily a change in the state 

 of the bodies, and that change a;ises from their inertia; is 

 not then inertia a force according to the author's own defi- 

 nition ? The forces of an acting, or resisting body, diifer 

 in nothing but the names which we assume, or according as 

 we fix the idea of agent, or patient to either of them. To 

 destroy motion, requires the same force as to produce it; 

 and since the quantity of motion produced by a body im- 

 pinging on one at rest, is precisely equal to that destroyed 

 by the bo y, which was at rest, the one may as properly be 

 said to be a force as the other; both bodies are inert, and 

 their force consists only in the resistance which each of them 

 makes, by reason of their impenetrability, to a change of 

 their condition as to motion or rest. But he says, that if it 

 were a force, it would be of some definite quantity ; and an 

 " impressed force less than that would not move the body." 

 This will apply only to particular kinds of forces, such as 

 that of cohesion, gravity, and active forces generally ; but 

 even these may as well be expressed by the force of mov- 

 ing bodies, or that of their inertia, as by any equivalent de- 

 finite force. The force of inertia being that which arises 

 from some change in the state of bodies as to motion or 

 rest, necessarily implies some motion or destruction of mo- 

 tion, even by the least force, as its adequate effect ; and the 

 quantity of motion produced, or the magnitude of the change, 

 is the true measure of that force, considered either as act- 

 ing or resisting. This force, though not constant, is defi- 

 nite, and is used in mechanics as the measure of force gen- 

 erally. This is so important an axiom in the science, that 

 it is astonishing that the author should doubt of its certainty. 



