33i 



REPORT — 1872. 



Coincidence Opposition 

 of phase of of phase of 

 M and N M and L 



theoretical value for nearly all places. On the other hand, the equilibrium - 

 theoretical ratio is fairly approximated to in the values found for Fort Point 

 and Kurrachec. 



50. The following Table exhibits the times of coincidence and opposition 

 of phase of some of the chief tides. The values are deduced from the 

 mean of the results when more than one year's observations have been 

 analyzed. 



Coincidence Coincidence 



of phase of of phase of 



S and M P and O 



Liverpool. "1 



Lat. 53°-40 N., long. Qh-SOW. J 



Eamsgate. 1 



Lat. 51°-3 N., long. 0''-09 E. j 



Portland Breakwater. 1 



Lat. 50°5 N., long. 0^-lQ W. J 



Kurrachee (India). \ 



Lat. 24<^-9 N., long. 4''47 E. J" 



Bombay (India). ] 



Lat. 18°-9j N., long. 41-86 E. / 



Fort Point (California). 1 



Lat. 37°-67 N., long. 8"-15 W./ 



Cat Island (Gulf of Mexico). I 

 Lat. 30°-23 N., long. 5^Qi W. j 



l-ioo 



1-070 



0-214 



0-535 



0-353 



0-790 



0'26o 



1-152 



1-846 



2-024 



-1747 



0-750 



-4-201 



0-126 



2-422 



The sign — indicates that the ph.enom3non occurs before the moon's perigee. 



The following is the investigation of the formula for semidiurnal and semi- 

 diurnal declinational tides : — 



Let YP and YS be the great 

 cii'cles in which a geocentric 

 spherical surface is cut by the 

 earth's equator and by the plane 

 of the orbit of sun or moon. 

 When the moon is considered, Y 

 -wiU be approximately the first 

 point of Aries. It is, of course, 1' 



rigorously so for the sun. 



Drawing SN perpendicular to YP, we have SjSr = S, the declination. Let 

 SyP=?, being the inchuation of the orbit to the equator. Suppose now Q 

 and P to be points of the equator in which it is cut by the meridian through 

 the crests of the semidiurnal equilibrium tide, and the meridian through the 

 place for which the equilibrium tide is to be expressed. If s denote the 

 equilibrium semidiurnal variation of tide-height, Ave find readily, from § 808 

 (23) of Thomson and Tait's ' Natural Philosophy ' 



s = c cos2 1 cos2 d cos (2 X QP), 



where c denotes a constant for each place. Take P' so that PP'=QN', and 

 join SP'. 



