54 The Rev. S. Haughton on the Solar and Lunar 



diurnal tide are the most perfect that have been ever made on 

 so large a scale and for such a length of time. 



Having thus eliminated the diurnal tide from the observed 

 heights, I constructed the diurnal tide at high and low water 

 following the moon's southing, by points, on paper ruled into 

 divisions of tenths of an inch ; on the scale of heights, of an inch 

 to the foot ; and of time, of five lunar days to the inch. After 

 joining the points, a curve was drawn in the usual way, which 

 represented geometrically the actual results of observation. These 

 cui'ves were then compared with other curves constructed from 

 theory in the following manner. 



From whatever theory of tides we set out, whether Equilibrium 

 theory, Laplace's dynamical theory, or Mr. Airy's theory of canal 

 waves, we arrive at the result that the diurnal tide is proportional 

 to the product of the sine and cosine of the declination of the 

 luminary ; and the most general form of diurnal tide may be 

 deduced from this supposition, combined with the well-known 

 fact that the tide does not accompany, but follows the southing 

 of the luminary ; and with the hypothesis of the hydrodynamical 

 theories, that the position of the luminary corresponding to any 

 tide is not its actual position, but the position it had at a period 

 preceding the period of the tide, by an interval called the age of 

 the tide. We may therefore consider the following expression as 

 the most general expression for the height of the diurnal tide ; 

 at least it is the expression deduced from theory with which I 

 have compared the observed diurnal tide, 



D = S sin 2(7 cos (s — 4) + M sin 2/a cos (m — f,„) . . (2) 

 In this equation, — 



D is the height of the diurnal tide at the high or low water 

 following the moon's southing, expressed in feet. 



S and ^I are the coefficients in feet of the solar and lunar 

 diurnal tides. 



a and /j, are the declinations of the sun and moon, at a period 

 preceding the high and low water, by an interval to be de- 

 termined for each luminary, and called the age of the solar 

 and lunar diurnal tide. 



s and m are the hour-angles of the sun and moon west of the 

 meridian at the time of high or low water. 



is and 2„, are the diurnal solitidal and lunitidal inteiTals, or 

 the time which elapses between the sun's or moon's south- 

 ing and the solar or lunar diurnal high water. 



The right-hand member of equation (2) therefore contains 

 eight quantities, of which two only, m and s, are known directly 

 by the observed time of apparent high and low water; the 



