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considered, or generally." He admits that while " the an 

 cicnts extracted all they could out of one line or surface 

 before passing to another," " the moderns, since Descartes, 

 emj^loy themselves on questions which relate to any figure 

 whatever." These facts are the reverse of what, according 

 to his theory, they should be. So, too, in mechanics. Be- 

 fore dividing it into statics and dynamics, M. Comte treats 

 of the three laws of motion, and is obliged to do so ; for 

 statics, the more ^ewera7 of the two divisions, though it 

 does not mvolve motion, is impossible as a science until the 

 laws of motion are ascertained. Yet the laws of motion 

 pertain to dynamics, the more special of the divisions. 

 Farther on he points out that after Archimedes, who dis- 

 covered the law of equilibrium of the lever, statics made 

 no progress until the establishment of dynamics enabled us 

 to seek " the conditions of equilibrium through the laws of 

 the composition of forces." And he adds — " At this day 

 this is the method universally employed. At the first glance 

 it does not appear the most rational — dynamics being more 

 complicated than statics, and precedence being natural to the 

 simpler. It would, in fact, be more philosophical to refer 

 dynamics to statics, as has since been done. " Sundry dis- 

 coveries are afterwards detailed, showing how completely 

 the develojDment of statics has been achieved by consider- 

 ing its problems dynamically ; and before the close of the 

 section M. Comte remarks that " before hydrostatics could 

 be comprehended under statics, it was necessary that the 

 abstract theory of equilibrium should be made so general 

 as to apply directly to fluids as well as solids. This was ac- 

 complished when Lagrange supplied, as the basis of the 

 whole of rational mechanics, the single princij^le of virtual 

 velocities." In which statement we have two facts directly 

 at variance with M. Comte's doctrine ; — ^first, that the sim- 

 pler science, statics, reached its present development only 

 by the aid of the principle of virtual velocities, which be- 



