HAEMONIC ANALYSIS AND PREDICTION OF TIDES. 115 



The process outlined below follows to some extent one of the methods 

 of Doctor Harris, extending his treatment for the components K and 

 to other components. 



The lengths of series may be taken the same as the lengths used as 

 the analysis of the hourly heights, which are 29, 58, 87, 105, 134, 163, 

 192, 221, 250, 279, 297, 326, 355, and 369 days. It is sometimes 

 convenient to divide a series, whatever its length, into periods of 29 

 days each. This permits a uniform method of procedure, and a com- 

 parison of the results from different series affords a check on the 

 reliableness of the work. 



The first process in this analysis consists in making the usual high 

 and low water reductions, including the computation of the lunitidal 

 intervals. Form 138 provides for this reduction. The times and 

 heights of the high and low waters, together with the times of the 

 moon's transits are tabulated. For convenience the standard time 

 of the place of observations may be used for the times of the high and 

 low waters, and the Greenwich mean civil time of the moon's transits 

 over the meridian of Greenwich may be used for the moon's transits. 

 The interval between each transit and the following high and low 

 water is then found, and the mean of all the high water intervals and 

 the mean of all the low water intervals are then obtained separately. 

 The true mean intervals between the time of the moon's transit over 

 the local meridian and the time of the following high and low waters 

 being desired, the means as directly obtained must be corrected to 

 allow for any difference in the kind of time used for the transit of 

 the moon and the time of the tides and also for the difference in time 

 between the transit of the moon over the local meridian and the 

 transit over the meridian to which the tabular values refer. 



A convenient table for the correction of the lunitidal intervals, 

 when the high and low waters have been given in standard time and 

 the moon's transits over the meridian of Greenwich are given in 

 Greenwich mean civil time, will be found in Special Publication 

 No. 26 of the U. S. Coast and Geodetic Survey. 



i If the tide is of the semidiurnal type, the approximate amplitude 

 and epoch for component Mj may be obtained directly from this high 

 and low water reduction. On account of the presence of the other 

 components the mean range from the high and low waters will always 

 be a little larger than twice the amplitude of M2. If the data are 

 available for some other station in the general locality, the ratio of 

 the M2 amplitude to the mean range of tide at that station may be 

 used in finding the M2 amplitude from the mean range of tide at the 

 station for which the results are sought. If this ratio can not be ob- 

 tained for any station in the general locality, the empirical ratio of 

 0.47 may be used with fairly satisfactory results. After the ampli- 

 tude of Mj has been thus obtained, it should be corrected for the 

 longitude of the moon's node by factor F from Table 12. 



The epoch of Mj may be obtained from the corrected high and low 

 water lunitidal intervals H WI, L WI by the following formula — 



M°2 = i-(fi'F/+LF7)x 28.984 + 90° (445) 



In the above formula fl^TF/must be greater than L WI, 12.42 hours 

 being added, if necessary, to the R WI as directly obtained from the 

 high and low water reductions. 



