MECHANICAL PHILOSOPHY. 423 



had been hitherto established by separate and independent 

 methods ; and the principles of the solution were in many cases 

 obscure and unsatisfactory. Newton traced the whole theory to 

 one fundamental principle, and thus raised Statics to the un- 

 doubted rank of a science. The principle of the composition of 

 motions had, it has been said, been assumed by Galileo, though no- 

 where formally stated in his writings. Newton felt the full force 

 and value of the principle, and combining it with the second law 

 of motion, which states . the proportionality of the force to the 

 motion generated, he gave the first formal proof of the celebrated 

 principle of the composition of forces. I shall not dwell upon the 

 objections which have been urged against this mode of establishing 

 the important theorem of the parallelogram of forces, nor upon 

 the attempts which have since been successfully made to assert 

 for this principle the dignity of an abstract truth. It is sufficient 

 at present to observe that the conditions of equilibrium, in the 

 different classes of simple machines, were shown by Newton to 

 flow easily and simply from this fertile principle ; and that it has 

 been since generally taken as the basis of statical science. 



But much as the doctrine of equilibrium is indebted to 

 Newton, the science of motion has received yet greater accessions 

 from his hand. We have already seen that some great steps 

 were made in this branch of mechanical science by Galileo and 

 Huygens ; and many important problems were solved by other 

 writers. Yet these were but so many detached spots in the wide 

 field of truth, reached by independent paths, and cultivated by 

 different processes. No highway had as yet been opened into its 

 fertile territory ; and its unexplored recesses were still as difficult 

 of approach, as if no part whatever had been subjugated to 

 human reason. This great want was supplied by Newton ; and, 

 in the first book of the Principia, he has developed, by general 

 and uniform methods, the laws of rectilinear and curvilinear 

 movement under the influence of a central force ; the theory of 

 the motion of bodies confined to given curves or surfaces, &c. 



But great and valuable as were these additions to dynamical 

 science, they seem to have been regarded by Newton but as steps 

 to that system of the universe, the key of which he had early 

 mastered. The principle of universal gravitation his grand dis- 

 covery is indeed the highest and most comprehensive physical 

 truth ever reached by man ; and we shall not mis-spend our time 



