HARMONIC ANALYSIS AND PREDICTION OF TIDES 101 
288. The lengths of series may be taken the same as the lengths 
used as the analysis of the hourly heights (see par. 152). It is some- 
times convenient to divide a series, whatever its length, into periods of 
29 days each. This permits a uniform method of procedure, and a 
comparison of the results from different series affords a check on the 
reliableness of the work. 
289. 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. 
290. If the tide is of the semidiurnal type, the approximate ampli- 
tude and epoch for M, may be obtained directly from this high and 
low water reduction. On account of the presence of the other con- 
stituents the mean range from the high and low waters will always 
be a little larger than twice the amplitude of M,. If the data are 
available for some other station in the general locality, the ratio of 
the M, amplitude to the mean range of tide at that station may be 
used in finding the M, amplitude from the mean range of tide at the 
station for which the results are sought. If this ratio cannot 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 M. has been thus obtained, it should be corrected for the 
longitude of the moon’s node by factor F' from table 12. 
291. The epoch of M, may be obtained from the corrected high and 
low water lunitidal intervals HWI, LWI by the following formula: 
M°.=3(HWI+LWI) X28.984+90° (426) 
In the above formula HWI must be greater than LW/J, 12.42 hours 
being added, if necessary, to the HW as directly obtained from the 
high and low water reductions. 
292. The difference between the average duration of rise and fall 
of the tide at any place, where the tide is of the semidiurnal type, de- 
pends largely upon the constituent My. It is possible to obtain from 
the high and low waters a constituent with the speed of M, which, 
when used in the harmonic prediction of the tides, will cause the mean 
duration of rise and fall to be the same as that at the station. The 
effect of M, upon the mean duration of rise will depend chiefly upon 
the relation of its amplitude and epoch to the amplitude and epoch 
of the principal constituent M,. By assuming an My, with epoch 
