haemoj^ic Analysis and PREDicTioisr of tides. 



103 



assigned may be readily obtained. The value of such division as 

 obtained directly from the formula will usually be a mixed number. 

 For Table 34 the nearest integral number, less any multiple of 24, is 

 used. 



The distribution of the daily sums for the analysis of the long- 

 period components may be conveniently accomplished by copying 

 such sums in Form 142 (fig. 25), taking the component divisions as 

 the equivalents of the component hours and using Table 34 to deter- 

 mine the division or hour to which each sum should be assigned. 

 The total sum and mean for each division may then be readily ob- 

 tained. These means can then be treated as the hourly means of the 

 short-period tides according to the processes outlined in Form 194 

 (fig. 29) with such modifications as will now be described. 



In using the daily means as ordinates of a long-period component 

 consideration must "be given to the residual effects of any of the short- 

 period components upon such means and steps taken to clear the 

 means of these effects when necessary. Component S2 mth a period 

 commensurate with the solar day, may be considered as being com- 

 pletely eliminated from each daily mean. Components K^ and Kj 

 are very nearly eliminated, because the component K day is very 

 nearly equal to the solar day. Other short-period components may 

 affect the daily means to a greater or less extent, depending largely 

 upon their amplitudes. Of these the principal ones are components 

 M2, N2, and Oj. In the distribution and grouping of the daily means 

 for the analysis of the several long-period components the disturbing 

 effects of the short-period components just enumerated, excepting 

 the effect of Mj upon MSf, will be greatly reduced, and in a series 

 covering several years may be practically eliminated. 



Because the period of MSf is the same as the synodic period of Mj 

 and S, there will always remain a residual efl'ect of the component Mj 

 in the component MSf sums of the daily means, no matter how long 

 the series, which must be removed by a special process. 



Let the equation of one of the short-period components be 



y = A cos {at-\-a) 



(416) 



Letting d = day of series, the values of t for the hours to 23 of d 

 day will be • 



24:{d-l), 24:{d-l) + 1, 24:{d~l) +2, .... 24(c?-l)+23. 



Substituting these values for t in (416) and designating the corre- 

 sponding values of the ordinate y as y^, y^, y2 • • • • 1/23 the following 

 are obtained: 



A cos [24:{d-l)a + a\ ' 



?/i =A cos[24:{d-l)a-\-a + a] 

 2/2 =Acos[24:id-l)a + a + 2a] 



y23 = A cos [24:{d-l)a-{-a + 2da] 



> (417) 



