286 Prof. G, H. Darwin. [June 19, 



it is not likely that such an evaluation will be attempted. But if 

 such a case is undertaken, the solar disturbance may be found by a 

 plan strictly analogous to that pursued below in the case of the 

 tides K 1} 0, P. The reader may be left to deduce the requisite 

 formulae from, the theory in 3. 



In the case of a long series of observations, each quarter year 

 should be reduced independently, and the mean values of H w cos K and 

 H n sin K H should be adopted as the values of the functions ; whence H n 

 and *: are easily found. The L tide is, of course, to be treated 

 .similarly. 



5. The Tide M 2 , 



This is the principal lunar tide. 



If we take the mean of n + 1 successive tides, the equations (9) give 

 us approximately 



-irSfc cos V m = A m , -TTS& sin V n = B m .... (16) . 



n + 1 



We here assume that in taking this mean over an exact number of 

 sjmi-lunations, the lunar elliptic tides, the solar tides, and the diurnal 

 tides are eliminated. 



With respect to the elliptic tides, this condition can only be ap- 

 proximately satisfied, becanse no small number of semi-lunations is 

 equal to a number of anomalistic periods, and the like is true of the 

 diurnal tides. In the example given below the diurnal tides are much 

 larger than the elliptic tides, and I have found by actual computation 

 (the details of which are not, however, given) that the disturbance in 

 the value of the M 2 tide arising from the diurnal tides is quite insen- 

 sible, and it may be safely accepted that the same is true of the dis- 

 turbance from the elliptic tides. 



With respect to the disturbance arising from the principal solar 

 tide S 2 , I find that it is adequately, although not completely, 

 eliminated by making the number n+1 of tides under summation 2 

 cover an exact number of semi-lunations. 



If the whole series of observations be short, it would be pedantic 

 to attempt a close accuracy in results, and we may accept these 

 formulae ; if the series be long, the residual errors will be gradually 

 completely eliminated. 



We have then 



E m cos m = A m , E m sin % m B m . 



If u m be the equilibrium argument at epoch, we have 



T> 



Whence K W = ^ + m , and H OT = 



*m 



