550 THE PK1NCIPLES OF SCIENCE. [criAr. 



which he could calculate the size of the moon's orbit, and 

 he then found the discrepancy to be inconsiderable. 



His theory of gravitation was thus verified as far as the 

 moon was concerned ; but this was to him only the begin- 

 ning of a long course of deductive calculations, each ending 

 in a verification. If the earth and moon attract each other, 

 and also the sun and the earth, there is reason to expect 

 that the sun and moon should attract each other. Newton 

 followed out the consequences of this inference, and showed 

 that the moon would not move as if attracted by the earth 

 only, but sometimes faster and sometimes slower. Com- 

 parison with Flamsteed's observations of the moon showed 

 that such was the case. Newton argued again, that as the 

 waters of the ocean are not rigidly attached to the earth, 

 they might attract the moon, and be attracted in return, 

 independently of the rest of the earth. Certain daily 

 motions resembling the tides would then be caused, and 

 there were the tides to verify the reasoning. It was the 

 extraordinary power with which Newton traced out geome- 

 trically the consequences of his theory, and submitted them 

 to repeated comparison with experience, which constitutes 

 his pre-eminence over all physicists. 



Quantities determined by T/ieory and not verified. 



It will continually happen that we are able, from certain 

 measured phenomena and a correct theory, to determine 

 the amount of some other phenomenon which we may 

 either be unable to measure at all, or to measure with an 

 accuracy corresponding to that required to verify the pre- 

 diction. Thus Laplace having worked out a theory of the 

 motions of Jupiter's satellites on the hypothesis of gravi- 

 tation, found that these motions were greatly affected by 

 the spheroidal form of Jupiter. The motions of the 

 satellites can be observed with great accuracy owing to 

 their frequent eclipses and transits, and from these motions 

 he was able to argue inversely, and assign the ellipticity 

 of the planet. The ratio of the polar and equatorial axes 

 thus determined was very nearly that of 13 to 14; and it 

 agrees well with such direct micrometrical measurements 

 of the planet as have been made ; but Laplace believed that 

 the theory gave a more accurate result than direct obser- 



