288 A SHORT HISTORY OF SCIENCE 



In computing the position of the centre of oscillation he arrives 



^r> 2 



at a fraction of the form ~ > where m denotes the mass of a 



particle, r its distance from the point of suspension. The nu- 

 merator is the so-called "moment of inertia," the denominator the 

 "statical moment" of later mechanics. He shows that the point 

 of suspension and the centre of oscillation are interchangeable. 



Finally he discusses the theory of centrifugal force, proving 

 that it varies as the square of the velocity and inversely as the 

 radius. This subject he also treated more fully in a special mono- 

 graph, published after his death when Newton had already given 

 a more general theory. His theorems are : 



1. When equal bodies move with the same velocity in unequal 

 circles, the centrifugal forces are to each other inversely as the diameters, 

 so that in the smaller circle the said force is greater. 



2. When equal movable bodies travel in the same or equal circles 

 with unequal velocities, the centrifugal forces are to each other as the 

 squares of the velocities. 



By experiments on a revolving sphere of clay which as he antici- 

 pated assumed a spheroidal form, he explains the observed polar 

 flattening of Jupiter. He infers that the earth must also be 

 flattened, and makes a numerical estimate in anticipation of future 

 verification. He explains the effect on a clock pendulum of trans- 

 porting it from Paris to an equatorial locality, where its weight is 

 opposed by an increased centrifugal force. 



Like Wallis (p. 290) and Sir Christopher Wren he accepted the 

 invitation of the Royal Society to attack the general problem of 

 impact. This led ultimately to the publication eight years after 

 his death of his On the Motion of Bodies under Percussion. 

 The theorems enunciated deal with various cases of central im- 

 pact, one of the most notable being : 



By mutual impact of two bodies the sum of the products of the 

 masses into the squares of their velocities is the same before and after 

 impact. 



