34 



interval between the upper, or visible, transits of the moon across the 

 meridian of a place is the mean lunar ofay of 24.841,202,4 mean solar 

 hours. 



61. It may be noted that the slow tilting to and fro of the plane of 

 the moon's orbit with respect to the plane of the earth's Equator 

 because of the changing longitude of the moon's node (par. 36) does 

 not affect the length of the mean lunar day, the mean speed of the 

 lunar hour angle, or the mean period of the travel of the moon from 

 intersection to intersection. The intersection moves to and fro along 

 the Equator in a small arc on either side of the equinox, its mean posi- 

 tion being the equinox itself. 



62. The mean periods and the speeds, or mean angular changes per 

 mean solar hour, of the movements of the sun and moon pertinent to 

 the development of the speeds of the tidal components are as follows: 



Table I 



Cycle 



Period in 



mean solar 



hours 



Speed in 

 degrees per 

 solar hour 



Mean solar day 



Mean lunar day 



Tropical month — moon's travel from intersection to corresponding intersec- 

 tion 



Anomalistic month— moon's travel from perigee to perigee (par. 43) 



Synodic month — full moon to full moon 



Tropical year — sun's travel, equinox to correspondin;; equinox 



Anomalistic year— sun's travel, perihelion to perihelion 



24 

 24.841,202,4 



655. 717. 96 

 661. 309, 20 

 708. 734, 1 



8765. 812, 7 



8766. 230, 9 



15 

 14. 492, 052, 1 



. 549, 016, 5 

 . 544, 374, 7 

 . 507, 947, 9 

 . 041, 068, 6 

 . 041, 066, 7 



63. The "speeds" in the preceding tabulation are the quotients of 

 360° divided by the corresponding period, in accordance with the de- 

 finition expressed in equation (28). The speed of the mean lunar 

 day is the mean hourly change in the angle between the hour circle 

 through the moon and the meridian of the place. The speed of the 

 tropical month is the mean hourly change in the angle between the 

 hour circle through the moon and that through the intersection of the 

 moon's orbit with the Equator. The sum of these two speeds is 

 therefore the mean hourly change between the meridian and the inter- 

 section. Similarly the sum of the speeds of the solar day and the 

 tropical year is the mean hourly change between the meridian of the 

 place and the equinox. Since the mean position of the intersection 

 is at the equinox, the two sums are the same, i.e., 

 15.000,000,0 14.492,052,1 



.041,068,6 .549,016,5 



15.041,068,6 



15.041,068,6 



