382 REPORT— 1872. 



/t or 2MS. Speed (2y— 40-4-2);). 2SM. Speed (2y4-2(T—4»/). 



MS. Speed (4y-2(T-2j)). SMS. Speed (47-6(7+21)). 



1851. ]857. 1866. 1870. 1851. 1857. 1866. 1870. 

 Bj 0-2660 02655 0-2618 0-2831 0-0517 00461 00391 o'0263 

 88°-i5 94°'4S 89°-43 930-26 i32°-i9 1350-62 i36°-74 i34°-5o 



Ci 



46. The complete separation of the mean lunar and mean solar semi- 

 diiu'nal tides in the foregoing analj'sis, together -with the respective epochs 

 of each tide, furnishes a ready means of finding the time of spring-tides 

 or the time at which the two tides are exactly the same in phase. If we 

 take, for instance, the respective epochs of these tides as given (§ 25) for 

 Eamsgate, we find that the mean solar semidiurnal tide attains its maxi- 

 mum when hi'ice the mean sun's hour-angle, or angular distance from the 

 meridian, is 32°-70. Similarly the mean lunar semidiurnal tide attains its 

 maximum when twice the mean moon's hour-angle is 339°-43. Dividing 

 the difference between these two epochs by twice the difference between 

 their respective mean daily motions, we obtain an interval Aihich represents 

 the time at which the two tides are coincident after the two bodies were in 

 conjunction. The difference between the mean daily motions of the moon 

 and sun is 12°-191 per day. The result thus obtained for Eamsgate is 



360° + 32°-70-339"-43 53°-27 oicr-i 



2xl2°-191 = 24^:382 = ^"^^^ ^'^'' 



47. Treating the solar diurnal dcclinatlonal tide (P) and the lunar diurnal 

 dcclinational tide (0) in a similar way, we obtain the interval after the 

 conjunction of the two bodies at which these tides are coincident in phase. 

 Thus, for instance, we find (§ 25) for Eamsgate 



262°-58-99°-34 163°-24 n oc,- i 



■ j^ = — — — = 6*69o days. 



2xl2°-191 24°-382 ^ 



4B. The lunar elliptic semidiurnal tides L and N, and the mean lunar 



semidiurnal tide M may also be similarly treated. The equilibrium theory 



gives 



'7c € 



7t{cos2(y~(T)<-l— 2 cos[2(y— e-)«— 0]— ■2Cos[2(y— ff)i-f-^]} 



for the sum of the mean lunar semidliu'ual and lunar elliptic semidiurnal 

 tides, where 7< denotes the semi-range of the mean lunar semidiurnal tide, 

 e the excentricity of the moon's orbit, and <p the longitude of the mean 

 moon (M) reckoned from the perigee, or, astronomically speaking, the 

 mean anomaly. "We have 



.^ = (<r-©)(i-T) 



