ISAAC NEWTON 93 



Newton also calculated the motions of the earth's axis, 

 and the consequences of them: viz., the precession of the 

 equinoxes, and the nutation superimposed upon this. 



A very remarkable conclusion was that the whole centre 

 of mass of the solar system was either at rest or in uniform 

 motion in a straight line. This is a great example of the 

 centre of mass principle, in part recognised by Huygens, 

 and fully set forth by Newton in his third law, according to 

 which the centre of mass of a system of bodies, or its 

 momentum, remains uninfluenced, when all forces and their 

 reactions only act within the system. Only when forces 

 act upon the system from without, forces whose reactions 

 operate outside the system, does the centre of mass ex- 

 perience an acceleration in accordance with the second law, 

 and the momentum undergo a corresponding change. 



These extensive investigations were rendered possible 

 for Newton by his discovery of a new method of calculation, 

 that of 'fluxions,' as he calls it; it was later called by 

 Leibniz the 'infinitesimal' or 'diflFerential and integral' 

 calculus. This is a method of reckoning with infinitely 

 small quantities, the need for which appeared very early. 

 Galileo was already obliged, in following out the simple 

 motion of free fall, to divide up the whole time of fall into 

 parts, in order to be able to consider the velocity in each 

 part of the time singly, and similar problems arise in the 

 investigation of every kind of motion. But since the velocity 

 changes uniformly, and not in jumps, strictly accurate 

 calculation requires the single periods of time to be infinitely 

 small, whereby the distances corresponding to them also 

 become infinitely small, and the question remains of how 

 we are to regard the relation between distance and time, the 

 velocity, as a relationship between two infinitely small 

 quantities, and how we are to calculate it. In the same way 

 in Descartes' calculation of the rainbow, and Mariotte's 

 calculation of the distribution of pressure in the earth's 



