14 NEWTON S PRINCIPIA. 



the force or power of matter to persist in any given 

 state, whether of rest or of motion in a straight line, and 

 to resist any external force impressed upon it to change 

 that state centripetal force., which is the power that 

 draws towards a given point or centre bodies at a distance 

 from it finally, the three kinds of amount of centripetal 

 force ; the absolute amount, in proportion to the intensity 

 of the power exerted in drawing towards the centre ; the 

 accelerating, in proportion to the velocity generated in a 

 given time; and the moving, in proportion to the motion 

 generated in a given time towards the centre.* 



Two things are worthy of remark in these definitions : 

 first, that, as if foreseeing the cavils to which his doc 

 trines would give rise, he guards, in a scholium, against 

 the supposition that he means to give any opinion respect 

 ing the nature or cause of centripetal force, much less 

 that he ascribes any virtue of attraction to mere centres 

 or mathematical points ; whereas he only means to express 

 certain known and observed facts : secondly, that, in 

 illustrating his definition of centripetal forces, he really 

 anticipates his great discovery ; for, after giving the 

 examples of magnetic action, and of a stone whirled in 

 a sling, he proceeds to the motion of projectiles, and shows 

 how, by increasing the centrifugal force, they may be made 

 to move round the earth, as may also, he says, the moon, 

 if she be a heavy body, or in any other way be deflected 

 towards the earth, and retained in her orbit. That force, 

 he adds, must be of a certain amount, neither more nor 

 less ; and the business of mathematicians is to find this 

 necessary amount ; or, conversely, having the amount 



* There are eight definitions in the book, though we have only given 

 them under seven heads, not having made a separate definition of the 

 force impressed, which is here mentioned under the important head of the 

 vis inertice. 



