12 



THE TIDAL PROBLEM. 



If a tidal protuberance has a position behind the moon's position, as at 

 B, a component of the moon's attraction tends to accelerate the earth's 

 rotation and to retard the moon's motion. If a protuberance rises directly 

 beneath the moon's position, its forward and backward pulls are equal. 



On the opposite side of the moon 

 there are complementary protu- 

 berances, as A', B', fig. 1, whose 

 rotatory effects are the reverse 

 of those on the moonward side, 

 but whose greater distances give 

 them less efficiency. It is merely 

 this difference in effectiveness 

 growing out of difference of dis- 

 tance that is usually appealed to 

 as influencing rotation. 



I shall endeavor to show later 

 that, while the foregoing reason- 

 ing seems to be unimpeachable in 

 itself, there are counterbalancing 

 factors which seem to have been 

 overlooked, and which nuUify the 

 value of this mode of treatment. 

 They do not, however, nuHify 

 the proposition that tidal friction 

 tends to retard the earth's rota- 

 tion. It seems best, however, to 

 review the subject first on the 

 accepted lines. 



The tides represented in fig. 1 

 are such as are assigned to the 

 direct pull of the tide-producing 

 body and are known as "direct." 

 The protuberance ^, fig. 1, repre- 

 sents a tide which is interpreted 

 as having lagged in its forma- 

 tion, and hence has been carried 

 forward by the rotation of the 

 earth to a position in front of 

 the moon's position; B represents 

 a tide which has been formed 

 behind the moon's position, but 

 both may be regarded as falling within the class of "direct" tides. This 

 class of tides are said to be built up when the natural free period of the 

 tidal wave is less than that of the tidal forces. If the natural free period 

 of the tidal wave is greater than that of the tidal forces, the tendency is to 

 produce " inverted" tides. The law underlying this difference of result, to 

 which Newton first directed attention, is thus stated by Darwin:^ 



Fig. 1. 



The Tides, pp. 171-172. 



