ISAAC NEWTON 91 



actual fact the force of gravity falls off from the earth's sur- 

 face to the moon, in accordance with the square of the dis- 

 tance, and hence that the force of gravity known from the 

 weight of objects upon earth is actually only a special case of 

 universal gravitation.* 



Newton also calculated the flattening of the earth at the 

 poles resulting from centrifugal force, at a time when the 

 opinion was still held by some that the earth is an ellipsoid 

 lengthened in the direction of the axis. He also calculated 

 the increase in the force of gravity on the earth's surface as 

 we pass from the equator to the poles, and thus explained 

 hitherto inexplicable observations concerning the change in 

 the rate of pendulum clocks when brought into other lati- 

 tudes; these observations could then be used to investigate 

 the form of the earth. It now became for the first time 

 directly obvious that, while weight and mass are exactly 

 proportional for all bodies at the same place, the weight of 

 any body can alter independently of its mass, a fact which 

 follows from the law of gravitation. 



An especially valuable achievement was the discovery of 

 the true and complete explanation of the tides of the sea, 

 which had been known from the earliest times. Galileo and 

 Kepler had striven after an explanation in vain, although 

 the latter already assumed an attraction exerted by the moon 

 upon the water of the earth, just as he also considered from 

 time to time an attractive force proceeding from the sun and 

 acting on the planets. The attractive force of the moon 

 could only explain the heaping up of the water on the side 

 turned towards it, but not the same effect, always simul- 

 taneously present, upon the side turned away from the moon. 

 All these phenomena result, as Newton showed, from the 

 simultaneous action of gravitation and centrifugal force, 

 the latter being produced by the fact that the earth also 

 revolves once a month, namely together with the moon about 



^ Principia, lib. 3, prop. 4. 



