$ i33] Libration; the Two New Sciences 175 



bodies are kept at rest by forces applied to them (statics), 

 and certain problems relating to the resistance of bodies 

 to fracture and to bending, though in both of these 

 subjects Galilei broke new ground. More important 

 astronomically and probably intrinsically also is what he 

 calls the science of local motion,* which deals with the 

 motion of bodies. He builds up on the basis of his early 

 experiments ( 116) a theory of falling bodies, in which 

 occurs for the first time the important idea of uniformly 

 accelerated motion, or uniform acceleration, i.e. motion 

 in which the moving body receives in every equal interval 

 of time an equal increase of velocity. He shews that the 

 motion of a falling body is except in so far as it is dis- 

 turbed by the air of this nature, and that, as already 

 stated, the motion is the same for all bodies, although 

 his numerical estimate is not at all accurate.t From this 

 fundamental law he works out a number of mathematical 

 deductions, connecting the space fallen through, the velocity, 

 and the time elapsed, both for the case of a body falling 

 freely and for one falling down an inclined plane. He 

 gives also a correct elementary theory of projectiles, in 

 the course of which he enunciates more completely than 

 before the law of inertia already referred to ( 130), 

 although Galilei's form is still much less general than 

 Newton's : 



Conceive a body projected or thrown along a horizontal 

 plane y all impediments being removed. Now it is clear by 

 what we have said before at length that its motion will 

 be uniform and perpetual along the said plane, if the plane 

 extend indefinitely. 



In connection with projectiles, Galilei also appears to 

 realise that a body may be conceived as having motions 

 in two different directions simultaneously, and that each 

 may be treated as independent of the other, so that, 

 for example, if a bullet is shot horizontally out of a 

 gun, its downward motion, due to its weight, is unaffected 



* Equivalent to portions of the subject now called dynamics or 

 (more correctly) kinematics and kinetics. 



f He estimates that a body falls in a second a distance of 4 

 "bracchia," equivalent to about 8 feet, the true distance being 

 slightly over 16. 



