1890.] Harmonic Analysis of Tidal Observations. 337 



where log tan \e = 9'0677, an absolute constant for all times and 

 places. With the values of f and |(X + Y) and $(W Z) given 

 above in (q) and (p), and with the values of H' and f + i just found, 

 there results 



L = -0-495, M = -0-214. 



Now 



io cos - 



We have found in (p) 



(W + Z) = -4-23, K X ~ Y ) = + 6 ' 3 . 



so that 



f H sin (&-i) = + 3-73, f H cos (&-) = + 6'09. 



Whence > i lies in the first quadrant, and 



Then H = L [KX-Y) -hM] sec (?,-) 



whence, reducing from inches to feet, 



H = 0-69 ft. 

 Again, 



Ko = f + Wo = ( -i)+i + Uo = 31'50-|-6 -52 + 3 -37 = 41-39, 



where the value of is taken from (q). 



(v.) Final Reduction of Mean Water Mark. 



We subtracted 99 inches from all the heights before using them, 

 and the mean of the heights was then + 3'51 inches. Hence mean 

 water is 102'51 inches, or 8'54 feet above the datum of the original 

 tidal observations. 



