362 HISTORY OF MECHANICS. 



had taken place somewhat earlier; and that law which is more par 

 ticularly expressed in D'Alembert's Principle (the equality of the 

 action gained and lost) was, it has been seen, rather led to by the 

 general current of the reasoning of mathematicians about the end of 

 the seventeenth century than discovered by any one. Iluygheus, 

 Marriotte, the two Bernoullis, L'Hopital, Taylor, and Hermann, have 

 each of them their name in the history of this'advance ; but we cannot 

 ascribe to any of them any great real inductive sagacity shown in what 

 they thus contributed, except to Huyghens, who first seized the prin- 

 ciple in such a form as to find the centre of oscillation by means of it. 

 Indeed, in the steps taken by the others, language itself had almost 

 made the generalization for them at the time when they wrote ; and it 

 required no small degree of acuteness and care to distinguish the old 

 cases, in which the law had already been applied, from the new cases, 

 in which they had to apply it. 



CHAPTER VI. 



SEQUEL TO THE GENERALIZATION OF THE PRINCIPLES OF MECHANICS. 

 PERIOD OF MATHEMATICAL DEDUCTION. ANALYTICAL MECHANICS. 



E have now finished the history of the discovery of Mechanical 

 Principles, strictly so called. The three Laws of Motion, gen- 

 eralized in the manner we have described, contain the materials of the 

 whole structure of Mechanics ; and in the remaining progress of the 

 science, we are led to no new truth which was not implicitly involved 

 in those previously known. It may be thought, therefore, that the 

 narrative of this progress is of comparatively small interest. Nor do 

 we maintain that the application and development of principles is a 

 matter of so much importance to the philosophy of science, as the 

 advance towards and to them. Still, there are many circumstances in 

 the latter stages of the progress of the science of Mechanics, which 

 well deserve notice, and make a rapid survey of that part of its history 

 indispensable to our purpose. 



The Laws of Motion are expressed in terms of Space and Number; 

 the development of the consequences of these laws must, therefore, be 

 pel-formed by means cf the reasonings of mathematics ; and the science 



