1890.] Harmonic Analysis of Tidal Observations. 



311 



G. Increments of Arguments in Various Times. 



The following table gives the increments of arguments of the several 

 tides in various periods, multiples of 360 being subtracted. This 

 table facilitates verification of the calculation of the harmonic con- 

 stants. 



Example. 

 (a.) Place, Time, Datum Level, and Unit of Length. 



The case choseu is three months of observation (in reality the tidal 

 predictions of the Indian Government) at Bombay, and the epoch is 

 O h , January 1, 1887. 



A datum at or very near mean water-mark is taken, so that all the 

 H.W. are positive and the L.W. negative. This datum is found by 

 taking the mean of all the H.W. and L.W. of the original observations. 

 In this case 99 inches was subtracted from all the tide heights. I 

 might more advantageously have subtracted 102 or 103 inches, but 

 99 inches was chosen from considerations applicable to my earlier 

 attempts, but which do not apply to the computation in its present 

 form. 



At places where there is a large annual inequality in the height of 

 water, it would be advisable to use a different datum for each quarter 

 of a year. It is not, however, important that the datum should con- 

 form rigorously to mean water-mark, for even the discrepancy of 

 3 inches, which occurs in my example, does not materially affect the 

 result. 



In recording the heights, a convenient unit of length is to be used, 

 and it is advantageous that the H.W. and the L.W. should be expres- 

 sible by two figures, so that the larger H.W. and L.W. shall fall into 

 the eighties and nineties. The unit of length is here the inch. 



