592 SCIENTIFIC RESULTS OK ZIEGEER POLAR EXPEDITION 



and different arguments are used for the various tides. From (47) to (50) we obtain the 

 following values, the heights being reckoned from mean sea level : 



Cape Flora Teplitz Bay 



Ft. Ft. 



Tropic HHW - . . . 0.537 0.621 (51) 



Tropic lyHW 0.410 0.446 (52) 



Tropic HLW —0.153 —0.419 (53) 



Tropic LLW —0.745 —0.648 (54) 



Mean sea level, as used above, is the mean of the hourly heights of the sea used for obtaining 

 the harmonic constants, or 



MSL= -^2'(A„ + /i, + /^, + h. + h^) (55) 



in which Ih represents the sum of all the heights throughout the series for the hour designated 

 by the subscript, and « = 24 times the number of days in the series discussed. As there is 

 usually a periodic variation in mean sea level from month to month, chiefly due to seasonal 

 changes in the direction and velocity of winds, which roughly complete their cycle in a year, 

 it must be borne in mind that when less than a year of record is analyzed the resulting mean 

 sea level is not a true mean for the station. 



This will be more evident from a study of the following table of mean sea levels on the 

 ist and 1 6th of each month during which observations were made : 



In the above table the heights are all referred to the tide staff at Cape Flora, that portion 

 which was obtained from the record at Teplitz Bay having been increased by 1.73 feet, the dif- 

 ference between the two staves as determined from simultaneous observations ; see (77). The 

 mean of the Teplitz Bay portion of the table, viz., April i to June i, is 5.86 feet on the Cape 

 Flora staff, or 5.86 feet — 1.73 feet = 4.13 feet on Teplitz Bay staff. The corresponding mean 

 for Cape Flora, June i to September i, is 6.08 feet. The difference in the mean sea level for 

 each of the two series is, therefore, 6.08 feet — 5.86 feet = 0.22 foot. The extreme difference in 

 the half-monthly mean sea levels of the table is 6.40 feet — 5.82 feet = 0.58 foot, or about 7 

 inches, in less than three months. 



Mean half-tide level is the mean of all the high and low waters for the period of observa- 

 tion. Abbreviating to initial letters, we have 



HTL 



(HW + LW) 



(56) 



When the harmonic constants for the station are known, the approximate valtie of mean 

 half -tide level may be computed by the formula 



HTL = MSIv + M, cos (2 M°, - M°,) - 0.04 ^^' ^ ^'''' cos (M°, - K°, - 0°J (57) 



