THE GROWTH OF PHYSICAL IDEAS 89 



in the same time and, therefore, with the same acceleration. 

 This discovery marks the beginning of the understanding of 

 the laws of motion. 



Another observation made by Galileo, that the time of 

 swing of a pendulum is constant, regardless of the extent 

 of the swing, and depends only upon the length of the 

 pendulum itself, involved inertia and the principle that 

 Newton embodied in his first law of motion— that a body at 

 rest cannot get into motion of itself and that a body in motion 

 tends to continue so with the same velocity unless it is acted 

 upon by external forces. This law led to the idea of mo- 

 mentum, the product of mass and velocity. Galileo was thus 

 able to define acceleration: "I call a motion uniformly ac- 

 celerated when, starting from rest, its momentum or degree 

 of speed increases directly as the time measured from the 

 beginning of motion." 



Newton embodied the same principle in his second law in 

 the following words: "The time of rate of change of mo- 

 mentum in any direction equals the moving force impressed 

 in that direction upon the mass particle." This second law 

 introduces the concept of mass as opposed to weight, which 

 was Galileo's concept. Galileo had realized, of course, that 

 matter has weight, but he did not realize that it was desirable 

 to have a term for the quantity of matter that a body con- 

 tains apart from the acceleration to which it is exposed. The 

 weight of a body is its mass under the acceleration of gravity. 

 In the first paragraph of his great book on natural philosophy, 

 however, Newton defined mass thus: "The quantity of matter 

 is the measure of the same arising from its density and bulk 

 conjointly. ... It is this quantity that I mean hereafter 

 everywhere under the name of body or mass." Thus a quan- 

 tity of mass remains the same, and under acceleration by 

 other means than gravity, the force is acting upon a given 

 mass rather than upon a given weight since the idea of weight 

 involves the acceleration of gravity. 



To the two fundamental laws of motion, Newton added a 

 third, which dealt with reaction and in some ways seems to 



