THE DEVELOPMENT OF MECHANICS 269 



results by stating the triangle of forces. These pioneers were followed 

 by a host of lesser investigators, and by the middle of the sixteenth 

 century this activity had resulted in the establishment of that branch 

 of mechanics which is now called statics. 



The next step was the introduction of the fundamental elements 

 of time and mass in an attempt to investigate the laws of motion. At 

 first little progress was made, as the misconception prevailed that a 

 constant supply of force was necessary to keep a body in motion. Pro- 

 longed experiment and investigation, however, gradually resulted in 

 a clearer understanding of these phenomena, and finally led to a correct 

 statement of the first law of motion by the great Italian philosopher 

 Galileo Galilei. Subsequent investigation of the motion of projectiles 

 and falling bodies led Galileo to the two great ideas of inertia and the 

 accelerating action of force, and enabled him to also state the second 

 and third laws of motion. In addition to these great discoveries, Galileo 

 generalized the law of equilibrium by stating the principle of virtual 

 velocities, thus giving the first general solution of all problems in 

 statics. 



For the next century the development of mechanics consisted chiefly 

 in an application of the principles of statics to liquids and gases. The 

 only notable advance in mechanical principles during this period was 

 made by Hu} r ghens, who, in connection with his invention of the 

 pendulum clock, investigated the center of oscillation and was thus 

 led to a more general statement of the third law of motion. 



The four fundamental ideas of space, time, force and mass were 

 now firmly established, but until the time of Newton found expression 

 only in an inorganic mass of facts and principles. Newton's discovery 

 of gravitation, however, led to such a broad generalization of these 

 ideas as to make possible a systematic treatment of the subject, and 

 mechanics as a science may be said to date from the publication of his 

 famous Principia in 1686. Newton's claim to preeminence, therefore, 

 rests not on the discovery of new mechanical principles, but on the 

 immeasurably greater service of bringing all natural phenomena under 

 the reign of universal law. 



Only one element was now lacking to complete the series of inde- 

 pendent fundamental statements necessary to constitute the foundation 

 of a complete system of mechanics. There still remained the estab- 

 lishment of a general relation between these fundamental concepts, 

 and after eighty years of experiment and investigation along the lines 

 indicated by Newton, this relation was furnished by d'Alembert in the 

 statement of his famous principle. 



This closed the first stage of development. The image was now 

 complete, and henceforth a system of mechanics based on this founda- 

 tion must be a purely deductive science. The subsequent history of 



