248 A SHORT HISTORY OF SCIENCE 



be stated as follows : A motion is said to be uniformly accelerated, when 

 starting from rest, it acquires, during equal time-intervals, equal in- 

 crements of speed. . . . 



The time in which any space is traversed by a body starting from 

 rest and uniformly accelerated is equal to the time in which that same 

 space would be traversed by the same body moving at a uniform speed 

 whose value is the mean of the highest speed and the speed just 

 before acceleration began. . . . 



The spaces described by a body falling from rest with a uniformly 

 accelerated motion are to each other as the squares of the time- 

 intervals employed in traversing these distances. . . . 



Galileo passes from falling bodies to pendulums, in which the fric- 

 tion of the inclined plane is absent and air resistance negligible. 

 He appreciates the possibility of utilizing the pendulum for time 

 measurement, and devises a simple apparatus for the purpose, 

 foreshadowing the invention of the clock. He discovers that the 

 time of vibration of the pendulum varies as the square root of 

 the length. 



He analyzes correctly the component motions of a projectile, 

 recognizing the law of the parallelogram of motion, as distinguished 

 from the parallelogram of forces discovered by Newton. He shows 

 that whether the initial direction of aim is horizontal or not, the 

 path described is a parabola with axis vertical, explicitly neglecting 

 air resistance and change of direction of vertical force. 



I now propose to set forth those properties which belong to a body 

 whose motion is compounded of two other motions, namely, one 

 uniform and one naturally accelerated ; these properties, well worth 

 knowing, I propose to demonstrate in a rigid manner. This is the kind 

 of motion seen in a moving projectile ; its origin I conceive to be as 

 follows: . . . 



A projectile which is carried by a uniform horizontal motion com- 

 pounded with a naturally accelerated vertical motion describes a 

 path which is a semi-parabola. Galileo, Two New Sciences. 



All this Dynamics was practically pioneer work of enormous im- 

 portance for the future of mechanics. 



