« 



4 

 f 



^. * X. 



348 -iP^<3/^ -4. I^' Bache on Tidal Observaiio7is. 



r 



diurnalj formed from the observations with the same displace- 

 ment of nine hours in the time of high water of the diurnal 

 curve; and corresponding to the epochs of the maximum dech- 

 nation, two, four, and six days before or after the maximum. 

 These show the general features of the curve sufficiently, and 

 the variations in the times and heights, the passage from single 

 to double tides, and the reverse ; and the coincidence with ob- 

 servations is such as to warrant a close numerical discussion. 



6. The equation of the curve shows how the time of high 

 and low water depends on the constants in the diurnal and semi- 



diurnal curve. 



Whewell 



C.cos 2f + D cos (Z-E)-y=-0, 



in which t is the time in hours from the place of the maximum 

 ordinate of the semi-diurnal curve as an origin ; C is the con- 

 stant of that curve of sines ; E is the distance of the maximum 

 ordinate of the diurnal curve for the former, and D the constant 

 for the curve of sines ; y is the ordinate of the complex curve. 

 By an easy transformation, this lakes the form; 



20. cos 2i+D cos if .cos E+D. sin ^.sin E-G=y. 



ForE=-9hrs. Cos E= -sin E= — -/J, 

 and y=2C cos H + D sin E (sin ^-cos ^) -C. 



The differential co-efficient of which for the case of the maxi- 

 mum or minimum is 



dy 



dt 



4C cos / . sin #-{-D sin E (sin /-f cos . /) = 

 11 40 40 



"T 



} 





sin t cos t D sin E D \/^' 



or, since the second term is negative when ty^ hours, 



4C 



cosec, / — sec t=^ — -^, 



Applying this to the four cases shown in the diagrams j 



hrs. min- 



E~9 hours, 0=^0175, D = 0-700 we find maximum at 10 25-4 



^0615 10 333 



= 0-400 10 511 



=0-157 11 56-8 



and for the intervals between high and low water in lunar hours 



h^ m, h. m. ii« m. h. in. 



9 09-2, 8 53-4, 8 17-8, and 6 06-4. 



We might apply this mode to test the hypothesis, using lor 

 the values of C, the half difference of the ordinates of six and 

 twelve hours from the mean, and of eighteen and twenty-fo*^^ 

 hours with the signs changed, and for D, the average of the or- 







