CHRISTIAN HUYGENS 77 



have been the velocities of the paths at the moment of separa- 

 tion, and hence also that of any given point of the undivided 

 pendulum, in order that the total centre of gravity shall only 

 reach the definite height. When this velocity is calculated, 

 the height from which the oscillation began being given, we 

 have the desired period of oscillation of the compound pen- 

 dulum, or also the length of the simple pendulum having the 

 same time of swing. 



When this calculation is made, a sum appears at an import- 

 ant point, formed of all the products of each mass particle of 

 the compound pendulum and the square of its distance from 

 the axis of rotation. This sum, first grasped by Huygens, 

 gives the key to the calculation of all rotational motion of 

 every kind; it later received the name of the 'moment of 

 inertia' of the body in question about the given axis. The 

 moment of inertia is the measure of the inertia for all 

 rotational motion, just as is the simple mass for all linear 

 motion. The part played in this case by the squares of the 

 distances of the single mass particles from the axis depends 

 upon the fact, as we can see from Huygens' argument, that 

 according to Galileo's laws of fall, the square of the velocity 

 of a body is a proportionate measure of the height to which it 

 is able to rise along any path - the choice of which makes no 

 difference - against its own weight, and that in the case of 

 rotary motion, the velocities are proportional to the distances 

 from the axis. 



Hence we find in the work of Huygens for the first time the 

 product of the mass and the square of the velocity appearing 

 as a quantity of importance for phenomena of motion. 

 Particularly in investigating the process of the collision of 

 elastic bodies, the importance of this product is made clear 

 by Huygens, inasmuch as he shows that the product in 

 question, when summed up for all bodies entering into col- 

 lision, is not altered by the latter, however the velocities 

 may change. It is true that Huygens generally uses the 



