L. Page — A Century's Progress in Physics. 303 



Art. X. — A Century's Progress in Physics; 

 by Leigh Page. 



Dynamics. — At the beginning of the nineteenth cen- 

 tury mechanics was the only major branch of physical 

 science which had attained any considerable degree of 

 development. Two centuries earlier, Galileo's experi- 

 ments on the rate of fall of iron balls dropped from the 

 top of the Leaning Tower of Pisa, had marked the origin 

 of dynamics. He had easily disproved the prevalent 

 idea that even under conditions where air resistance is 

 negligible heavy bodies would fall more rapidly than 

 light ones, and further experiments had led him to con- 

 clude that the increase in velocity is proportional to the 

 time elapsed, and not to the distance traversed, as he had 

 at first supposed. Less than a century later Newton had 

 formulated the laws of motion in the same words in 

 which they are given to-day. These laws of motion, 

 coupled with his discovery of the law of universal gravi- 

 tation, had enabled him to correlate at once the planetary 

 notions which had proved so puzzling to his predecessors. 

 His success gave a tremendous stimulus to the develop- 

 ment and extension of the fundamental dynamical prin- 

 ciples that he had brought to light, which culminated in 

 the work of the great French mathematicians, Lagrange 

 and Laplace, a little over a hundred years ago. 



Newton's laws of motion, it must be remembered, 

 apply only to a particle, or to those bodies which can be 

 treated as particles in the problem under consideration. 

 In his "Mecanique Analytique" Lagrange extended 

 these principles so as to make it possible to treat the 

 motion of a connected system by a method almost as sim- 

 ple as that contained in the second law of motion. 

 Instead of three scalar equations for each of the innumer- 

 ably large number of particles involved, he showed how 

 to reduce the ordinary dynamical equations to a number 

 equal-to that of the degrees of freedom of the system. 

 This is made possible by a combination of d'Alembert's 

 principle, which eliminates the forces due to the connec- 

 tions between the particles, and the principle of virtual 

 work, which confines the number of equations to the num- 

 ber of possible independent displacements. The aim of 

 Lagrange was to make dynamics into a branch of 



