6 THE LIMITATIONS OF SCIENCE 



geometry gives us a solution of the problem, which, 

 while it may not be the true solution, approximates to 

 the truth as nearly as we please. This is accom- 

 plished by dividing the path of a moving body into sec- 

 tions so small that the ratio of any of these infinitesimal 

 distances to the time necessary to traverse it, or the 

 velocity, is constant and finite. Newton had discov- 

 ered and verified the law of universal gravitation, and 

 had also collected the data of the action of forces on 

 bodies, and embodied them in three laws which still 

 serve as the postulates for the science of dynamics; 

 and D'Alembert supplemented them by a general 

 dynamic law of the motion of a system of bodies 

 acted upon by forces which embraced all the hitherto 

 isolated problems of this character, and reduced them 

 to a special and simple case of statics. 



On the theoretic side, Kant, Lagrange, and others 

 had discussed the general axioms of mechanics, and 

 had established the three fundamental units length, 

 mass, and time; and it is generally conceded that the 

 solution of any problem of mechanics into the simplest 

 combination of these three quantities is incapable of 

 further reduction. 



But one thing remained before an imposing structure 

 could be raised which should withstand criticism, and 

 that was a general law to include and solve problems 

 relating to a system of bodies in equilibrium and at 

 rest. And Lagrange accomplished this. 



