THE EVOLUTION OP SATELLITES. 113 



it was pointed out that wlieu tliere is no fluid friction we must put the 

 moon at M', but when there is friction she must be at M. Accordingly, 

 if there is no friction it is high tide when the moon is over the observer's 

 head, but when there is fluid friction the moon has passed his zenith 

 before he reaches high tide. Hence he woukl remark that fluid friction 

 retards the time of high water.' 



A day is the name for the time in whicli the earth rotates once, and 

 a month for the time in which tlie moon revolves once. Then, since 

 tidal friction retards the earth's rotation and the moon's revolution, we 

 may state that both the day and the month are being lengthened, and 

 that these results follow from the retardation in the time of high tide. 

 It must also be noted that the spiral in which the moon moves is an 

 increasing one, so that her distance from the earth increases. These 

 are absolutely certain and inevitable results of the mechanical inter- 

 action of the two bodies. 



At the present time the rates of increase of the day and month are 

 excessively small, so that it has not been found possible to determine 

 them with any approach to accuracy. It may be well to notice in 

 passing that if the rate of change of either element were determinable 

 that of the other would be deducible by calculation. 



The extreme slowness of the changes within historical times is estab- 

 lished by the records in early Greek and Assyrian history of eclipses 

 of the sun which occurred on certain days and at certain places. IsTot- 

 withstanding the changes in the calendar, it is possible to identify the 

 day according to our modern reckoning, and the identification of the 

 lilace presents no difficulty. Astronomy aflbrds the means of calculat- 

 ing the exact time and place of the occurrence of an ecliiDse even three 

 thousand years ago, on the supposition that the earth spun at the same 

 rate then as now, and that the complex laws governing the moon's 

 motion are unchanged. The particular eclipse referred to in history is 

 known, but any considerable change in the earth's rotation and in the 

 moon's motion would have shifted the position of visibility ou the earth 

 from the situation to which modern computation would assign it. Most 

 astronomical observations would be worthless if the exact time of the 

 occurrence were uncertain, but in the case of eclipses the place of 

 observation aftbrds just that element of precision which is otherwise 

 wanting. As, then, the situations of the ancient eclipses agree fairly 

 well with modern computations, we are sure that there has been no 

 great change within the last three thousand years either in the earth's 

 rotation or in the moon's motion. There is, however, a small outstand- 

 ing discrepancy which indicates that there has been some change. But 

 the exact amount involves elements of uncertainty, because our knowl- 



'This must not be considered as a fair statement of the case when the oceans are 

 as shallow as in actuality. The reader must accept the assurance that the friction of 

 the tides of shallow seas also causes retardation of the planet's rotation, although in 

 a somewhat different uuinner from that explained above. 

 SM 97 8 



