MECHANICAL PHILOSOPHY. 429 



was that which clothed the processes of dynamics in the symbolical 

 language of analysis. In order to accommodate his discoveries 

 to the actual state of mathematical knowledge, Newton chose to 

 exhibit them in a geometrical form, and by the aid of a new 

 doctrine which he had invented for the purpose. Thus his re- 

 sults are deprived of that elegance of form which is, in so eminent 

 a degree, characteristic of the conclusions of analysis ; and the 

 method of inquiry itself, in the higher and more difficult problems, 

 becomes elaborate and revolting. It must therefore be considered 

 an important era in mechanical science, when it received the aid of 

 the fluxional or differential calculus, the powerful instrument of 

 Newton's own invention, and when its principles were developed 

 by the fixed and uniform processes of analysis. This application 

 of the calculus to mechanical questions was made at an early 

 period, and by several hands ; but the systematic development 

 of the science in this new form is perhaps to be dated from the 

 publication of the mecanique of D'Alembert, in the year 1743. 



In what relates to the discovery of important principles, much 

 was also done. So early as the year 1592, in a short treatise on 

 mechanical science, Galileo had reduced the equilibrium of the 

 simple machines to a single principle ; and showed that the power 

 and the equilibrating weight are to one another inversely as the 

 spaces which they tend to describe in the same time. This is a 

 limited case of the general principle which has since been assumed 

 by Lagrange, as the basis of the whole of statical science the 

 principle of virtual velocities. The principle itself was first stated, 

 in all its generality, by John Bernoulli, in the year 1717. 



The science of motion was destined to receive a yet greater 

 extension by the accession of a general principle. The dynamical 

 problems, of which we have hitherto spoken, are those in which 

 the several parts of the body acted on are urged alike, and all 

 partake of a common movement. There are, it is true, many and 

 important problems in which this simplification is admissible : but 

 there are many cases, also, in which the parts of the body, in 

 virtue of their 'mutual connexion, are not free to obey the forces 

 which act externally upon each ; and to these the existing theories 

 did not apply. The first problem of this kind that engaged the 

 attention of mathematicians was the famous one proposed by 

 Mersenne the determination of the centre of oscillation of a 

 compound pendulum ; or, in other words, the investigation of 



