28 MR. AIRY ON THE LAWS OF THE TIDES 



and, on the same day when both vanish, 



/3 must = d '— O'+B and rtsin{ a '-— 0'+A} must = — ^ ; 

 by which the expression for diurnal tide at high water is changed to 



a.sin{ c '— o'-|-B}.sin{ c -O+A}— «.sin{ c '— o'+A}.sin{ d — 0+B} 



=fl.sin(B— A).sin{ d — O — d '— O'}, 

 and that at low water is changed to 



fl.cos{ ([ '- o'+B}.sin{ d — O +A} — a.sin{ d '— o'+A}.cos{ d — O +B} 

 =a.cos(B— A).sin{ d — O — d '— G'}. 

 The maximum of the compound diurnal tide at high water will then be a.sin(B— - A), 

 and that at low water a.cos(B— A). From the observed values of these maxima we 

 may obtain the values of a and B — A ; but we cannot from these obtain either A or B, 

 or a.sinjS, or h ; and thus the separation of the solar and lunar diurnal tides is in 

 this case impossible. 



As it seemed probable that the same value of a {7^ 13*"), which was inferred from 

 these stations, would apply to the other stations also, I changed the equations for 

 w, X, 1/, z, to the form corresponding to a^7'' 13™. But, on attempting to solve 

 them for Kilbaha, Kilrush, &c., I was entirely baffled. I could not in any instance 

 approach to a solution. 



As a last resource I resorted to the following method. Although the observations 

 cannot be supposed competent to furnish more than four unknown quantities, yet 

 they may be combined, and with sufficiently favourable coefficients, for the determi- 

 nation of the six quantities w, x, wy, wz, xy, xz\ as the equations will be simple, 

 values can certainly be found for these quantities ; and then the accuracy of the re- 



suits will be tested by ascertaining whether the following equations hold; — - = — , 



— ^=— • In this manner then equations were formed and solved for the principal 



Stations ; but at none of them was there any approach towards satisfying the equa- 

 tions of condition which I have just given ; nor even upon reducing the results to a 

 common phase of the diurnal tide-wave, by means of the intervals of diurnal esta- 

 blishment to be given in Section IX., and taking the mean, was there any approach 

 towards satisfying those equations. This is the last attempt that I made, and I con- 

 fess myself, on the whole, completely unsuccessful. 



The following considerations may perhaps explain the failure of all these attempts. 

 We have seen that when the days of evanescence, of diurnal tide in semidiurnal high 

 water, and of diurnal tide in semidiurnal low water, coincide, it is absolutely impos*- 

 sible to extract from the equations a result relating to the distinction of solar and 

 lunar effects. It may therefore be inferred that, when the days of evanescence 

 nearly coincide, the determination of the quantities sought will be nearly impossible, 

 or will be liable to very great errors. Now, at all the stations the interval between 



