TIDAL OBSERVATIONS. 383 



if T denotes the time of perigee preceding t : and so the preceding becomes 



7e 

 h{cos2(y-a)t+-^cosl{2y-3a + u)t + (<j—!u)T] 



— ncos [(2y — ff— ct)<— (<r— ■z<7)T]} 

 or 



7i{cos2(y-<T)<+ ^^cos [(2y-3<r+t!r)<+(<T-^)T] 



+ f cos[(2y - ff_^)< + lSO°-(ff-^)T]}, 



showing that <=T is the time of coincidence of the M and jST tides, and the 

 time of opposition of the M and L tides. Let 



E, cos{2(y- (7)<-eJ +E; cos [(2y~3o-+ tr)<-e;] 



' -R;'cos[(2y-ff-^)<-e;'+180°] 



he the expression for these constituents derived from observation. For the 

 times of coincidence we have 



M and N observation, 2(y — <t)<— e2=(2y— 3(7 + 'n^)<— e/, 

 giving t= 





€ — 6 



and therefore the delmi = — ^ — T : 



•^ cr — -ar 



similarly the delay of opposition of the M and L observed tides, after the 

 opposition of the corresponding equilibrium tides, is 



e,"-f, + 180°_^ 

 a — •or 



If, however, the corrected epochs are used, the term T should be omitted. 

 Thus for Eamsgate (§ 25) we have for the dday of coincidence of phase 

 between the M and N" tides 



339°-43-310°-31 29°-12 „ oon i a +-u > • 

 13°-06o ~ r3°<K35 —^'^~^ ^^5"^ "/'^'' *^° i^oon's perigee; 



and for the delay of opposition of phase between the M and L tides 



18G°-2S-339°-43 + 180° 26°-8.5 „ ^ , , , , . 

 1S°-Q65 = loo.opg =2"056 days vjUr the moons perigee, 



The solar elliptic semidiurnal tides E and T may be referred in a similar 

 manner to the mean solar semidiurnal tide (S). 



49. It is here worthy of remark, that the larger (K") lunar elliptic 

 semidiurnal equilibrium-tide (as indicated above) is seven times the value 

 of the smaller component (L) ; but on reference to the foregoing results 

 it will be found that the proportion between the actual components for 

 English x^orts is about 3^ to 1. The cause of this discrepance has not yet 

 been discovered : as will be seen subsequently (§ 51), the deduced value of 

 the smaller component L is too large when compared with its equilibrium- 



