208 THE PEINCIPLES OF SCIENCE. [chap. 



of the ordinary tidal waves. A tidal wave again gives 

 beautiful evidence of an effect of the law of gravity, 

 which we could never in any other way detect. Newton 

 estimated that the moon's force in moving the ocean is 

 only one part in 2,871,400 of the whole force of gravity, 

 so that even the pendulum, used with the utmost skill, 

 would fail to render it apparent. Yet, the immense extent 

 of the ocean allows the accumulation of the effect into a 

 very palpable amount ; and from the comparative heights 

 of the lunar and solar tides, Newton roughly estimated 

 the comparative forces of the moon's and sun's gravity at 

 the earth.' 



A few years ago it might have seemed impossible that 

 we should ever measure the velocity witli which a star 

 approaches or recedes from the earth, since the apparent 

 position of the star is thereby unaltered. But the spec- 

 troscope now enables us to detect and even measure such 

 motions with considerable accuracy, by the alteration which 

 it causes in the apparent rapidity of vibration, and conse- 

 quently in the refrangibility of rays of light of definite 

 colour. And while our estimates of the lateral move- 

 ments of stars depend upon our very uncertain know- 

 ledge of their distances, the spectroscope gives the motions 

 of approach and recess irrespective of other motions except- 

 ing that of the earth. It gives in short the motions of 

 approach and recess of the stars relatively to the eartli.^ 



The rapidity of vibration for each musical tone, having 

 been accurately determined by comparison with the Syren 

 (p. 10), we can use sounds as indirect indications of rapid 

 vibrations. It is now known that the contraction of a 

 muscle arises from the periodical contractions of each 

 sej^arate fibre, and from a faint sound or susurrus which 

 accompanies the action of a muscle, it is inferred that each 

 contraction lasts for about one 300th part of a second. 

 Minute quantities of radiant heat are now always measured 

 indirectly by the electricity which they prt)duce when falling 

 u[)on a thermopile. The extreme delicacy of the method 

 seems to be due to the power of multiplication at several 

 points iti the apparatus. The number of elements or junc- 



^ Principia, bk. iii. Prop. 37, Corollaries, 2 and 3. Mottc'a 

 translation, vol. ii. p. 310. 



- Roscoe's Spectrum Analysis, ist ed. p. 296. 



