SEQUEL TO THE GENERALIZATION. 381 



pertuis conceived that lie could establish a priori, by theological argu- 

 ments, that all mechanical changes must take place in the world so as 

 to occasion the least possible quantity of action. In asserting this, it 

 was proposed to measure the Action by the product of Velocity and 

 Space ; and this measure being adopted, the mathematicians, though 

 they did not generally assent to Maupertuis' reasonings, found that his 

 principle expressed a remarkable and useful truth, which might be 

 established on known mechanical grounds. 



15. Analytical Generality. Connection of Statics and Dynamics. — 

 Before I quit this subject, it is important to remark the peculiar char- 

 acter which the science of Mechanics has now assumed, in consequence 

 of the extreme analytical generality which has been given it. Sym- 

 bols, and operations upon symbols, include the whole of the reasoner's 

 task ; and though the relations of space are the leading subjects in the 

 science, the great analytical treatises upon it do not contain a single 

 diagram. The Mecanique Analytique of Lagrange, of which the first 

 edition appeared in 1*788, is by far the most consummate example of 

 this analytical generality. " The plan of this work," says the author, 

 " is entirely new. I have proposed to myself to reduce the whole the- 

 ory of this science, and the art of resolving the problems which it in- 

 cludes, to general formulas, of which the simple development gives all 

 the equations necessary for the solution of the problem." — " The reader 

 will find no figures in the work. The methods which I deliver do not 

 require either constructions, or geometrical or mechanical reasonings ; 

 but only algebraical operations, subject to a regular and uniform rule 

 of proceeding." Thus this writer makes Mechanics a branch of Anal- 

 ysis ; instead of making, as had previously been done, Analysis an 

 implement of Mechanics. 15 The transcendent generalizing genius of 

 Lagrange, and his matchless analytical skill and elegance, have made 

 this undertaking as successful as it is striking. 



The mathematical reader is aware that the language of mathemat- 

 ical symbols is, in its nature, more general than the language of words : 

 and that in this way truths, translated into symbols, often suggest their 

 own generalizations. Something of this kind has happened in Me- 

 chanics. The same Formula expresses the general condition of Statics 

 and that of Dynamics. The tendency to generalization which is thus 

 introduced by analysis, makes mathematicians unwilling to acknowl- 



1C Lagrange himself terms Mechanics, " An Analytical Geometry of four dimen- 

 sions." Besides the three co-ordinates which determine the place of a body in space, 

 the time enters as & fourth co-ordinate. [Note by Litfrow.] 



