262 POPULAR SCIENCE MONTHLY. 



ling the paper into a solid ball, it could be made to fall as rapidly as a 

 ball of wood or iron. Experiments of this nature led Galileo to the 

 discovery of the first law of motion, to wit: The velocity of falling 

 bodies varies directly as the time. 



At the beginning of the fall the velocity is zero; at the end of the 

 first second, it is a certain quantity which experiment shows to be the 

 same for all bodies. Let us call this velocity g. Galileo's experiments 

 showed that at the end of the second second the terminal velocity was 

 2g, at the end of the third, Sg and so on. The algebraic expression of 

 the first law is, then, 

 (I.) v = g.t 



(experiment shows that # = 9.81 meters approximately). 



The second law of motion refers to the relation of the spaces 

 through which the body falls in different intervals of time ; it is : The 

 spaces through which a body falls vary as the squares of the times. All 

 bodies obey this law, also, no matter of what materials they are made 

 up. 



(II.) s = ig.P 



(s = space, £ = time). 



At the beginning of the fall the time (t) is zero, and the velocity 

 (v) is also zero. At the end of the first second, t = I and v = g (by 

 I.). The velocity has increased from to g and its average value is 

 therefore 0-\-g/2=%g. The space traversed at the end of the first 

 second is (by II.) \g; at the end of the second second, 2g ; at the end 

 of the third second, \g, and so on. The two laws are not independent 

 but are separated for convenience. They are sometimes united into 

 one, and the law of inertia (also known to Galileo) added in this form: 

 Every body preserves its state of rest or of uniform motion in a right 

 line unless it is compelled to change that state by forces impressed 

 thereon.* 



It is this latter law that changed the whole face of science. It was 

 supposed by the ancients and by Copernicus that the normal condition 

 of all bodies was rest; that if they were moving it was because some 

 force was perpetually impelling them. On the earth a pendulum stops 

 because of the resistance of the air and the friction at its supports. 

 Remove the air and annul the friction and it will swing forever until 

 some impressed force stops it, so Galileo announced. Kepler was in- 

 cessantly trying to conceive how a planet could continue to move in its 



* The statement of the law is Newton's. It is implicit in Galileo's laws 

 of falling bodies and must have been understood by Leonardo da Vinci. Kepler, 

 perhaps, anticipated Galileo in its discovery. It is a necessary part of 

 Huyghens's theory of central forces, but it was not clearly enunciated until the 

 day of Newton. , 



