148 RECORD AND RESULTS OF 



Hence average rise and fall of tide 7.7 feet; at Van Rensselaer Harbor this 

 quantity was 7.9 feet. 



Height of highest high water level . . . . 24.6 feet 

 Height of lowest high water level .... 11.3 feet 



Hence extreme fluctuation in high water level 7.3 feet ; at Van Rensselaer Har^ 

 bor the corresponding quantity was 8.4 feet. 



Height of highest low^ water level .... 16.0 feet 

 Height of lowest low water level . . . .10.8 feet 



Hence extreme fluctuation in low water level 5.2 feet ; at Van Rensselaer Harbor 

 the corresponding quantity was 9.0 feet. 



The extreme fluctuation in the water level observed was 13.8 feet; at Van 

 Rensselaer Harbor this quantity was 16.6 feet. 



The mean establishments at the two places compare as follows : — 

 Mean establishment of high water at Port Foulke, ll*" 13". 8 



Mean establishment of high water at Van Rensselaer Harbor, 11 43.3 Diff. 29". 5 



Mean establishment of low water at Port Foulke, 17 19.5 



Mean establishment of low water at Van Rensselaer Harbor, IT 48.0 Diflf. 28". 5 



The determination of the constants, in the formula for half-monthly inequality, in 

 time, is as follows : — 



For high water: By interpolation, the mean interval occurs at O*" 38".4, hence a = 9° 36' 

 For low water : By interpolation, the mean interval occurs at 42.0, hence a = 10 30 

 For high water: By a graphical process the greatest range in the interval is 1'' 25" = 21° 15' 



its sine' is 0.3624 

 For low water : By a graphical process the greatest range in the interval is 1'' 26" = 21° 30' 



its sine is 0.3665 

 The mean establishment for high water 7.' = 11" 13". 8 = 168° 27' 

 The mean establishment for low water 17 19.5 = 259 52^ 



We have consequently the following expressions : — 

 From 131 observed high waters, 



tan 2 (6'- 168° 27') = - 0-3624 .m 2 (<?>- 9° 36;) 

 ^ ^ 1 + 0.3624 cos 2 (<?) — 9^ 36') 



and from 129 observed low waters 



tan 2 (0'-^ 259° 52^') = - _0j6 65 .m 2 ( ,^^-10° 30') 

 ^ ^ ^ 1 + 0.3665 cos 2{<p— 10° 30') 



By means of these expressions the inequality in time has been computed, the 

 agreement with observation is shown in the following table, also by the two diagrams 

 in which the observed quantities are indicated by dots. 



' In the manner in which — is deduced above it is preferable to use the sine instead of the tangent, 



as by Mr. Lubbock's process. See also Phil. Trans. 1836 (4th series of papers on Tides), by the 

 Rev. W. Whewell. 



