42 The Rev. Samuel Haughton on the Solar and Lunar 



ing, 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 curves were then com- 

 pared with other curves constructed from theory in the following way. 



From whatever theory of tides we set out, whether the 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 

 Diui-nal Tide may be deduced from this supposition, combined with the well- 

 known fact that tlie 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 as the 

 most general expression for the height of the Diurnal Tide ; at least it i« the 

 expression deduced from theory, with which I have compared the observed 

 Diurnal Tide : 



D = S sin 2of cos (s — i,) +Msm2fi. cos (m — i,n). (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 31 are the coefficients, in feet, of the Solar and Lunar Diiurnal Tides. 



a and ju are the declinations of the Sun and Moon, at a period preceding the 

 High and Low Water, by an interval to be determined for each luminary, 

 and called the Age of the Solar and Lunar Diurnal Tide. 



s and in are the hour-angles of the Sun and Moon, west of the meridian, at the 

 time of High or Low Water. 



i, and i„ are the Diurnal solitidal and lunitidal intervals, or the time which 

 elapses between the Sun's or Moon's southing, and the Solar or Lunar Diur- 

 nal 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 appa- 



