Revietvs and JS^otices of Books. 



121 



A remarkable consequence follows immediately from this 

 view of the second law. Since forces are measured by tbe changes 

 of motion they produce, and their directions assigned by the 

 directions in which these changes are produced ; and since the 

 changes of motion of one and the same body are in the directions 

 of, and proportional to, the changes of velocity, a single force, 

 measured by the resultant change of velocity, and in its direction, 

 will be the equivalent of any number of simultaneously acting 

 forces. Hence, 



'* The resultant of any number of forces (^applied at one point) 

 is to be found by the same geometrical process as the resultant of 

 any number of simultaneous velocities.*' 



After stating the third law of motion, whicb asserts the equality 

 of action and reaction, the authors then deduce, as immediate 

 consequences of the second and third laws, the following amongst 

 other important propositions : — 



" (a) The centre of inertia of a rigid body moving in any 

 manner, but free from external forces, moves uniformly 

 in a straight line. 

 " (6) When any forces whatever act on the body, the motion 

 of the centre of inertia is the same as it would have 

 been had these forces been applied, with their proper 

 magnitudes and directions, at that point itself.'' 

 We present the following as the authors' view of the conserva- 

 tion of energy : — 



" A limited system of bodies is said to be dynamically con- 

 servative^ if the mutual forces between its parts always perform or 

 always consume the same amount of work during any motion 

 whatever by which it can pass from one particular configuration 

 to another. The whole theory of energy in physical science is 

 founded on the following proposition : — 



" If the mutual forces between the parts of a material system 

 are independent of their velocities, whether relative to one another 

 or relative to any external matter, the system must be dynami- 

 cally conservative. 



" For if more work is done by the mutual forces on the different 

 parts of the system in passing from one particular configuration 

 to another, by one set of paths than by another set of paths, let 

 the system be directed, by frictionless constraint, to pass from the 

 first configuration to the second by one set of paths and return 

 by the other, over and over again for ever. It will be a con- 

 tinual source of energy without any consumption of material, 

 which is impossible." 



We have only time to direct the reader's attention to the 

 beautiful proof given in page 40, that " a particle attracted to a 



NEW SERIES. VOL. XIX. NO. T. JANUARY 1864. Q 



