HARMONIC ANALYSIS AND PREDICTION OF TIDES 43 
mean value of this factor is represented by the product sin w cos? 4 w 
cos‘ 44 2.307, which equals 0.38001.52, or 0.5776. When 
deriving the node-factor formula for M,, Darwin inadvertently omitted 
the factor 2.307 and obtained the approximate equivalent of the 
following: 
sin I cos*t 
sin I cos*}1 ae I 
sin w cost w cos*d2 x 1/Q.=—9 3800 — X 1/Q2 (206) 
J(M)) = 
Comparing the above with formula (75), it will be noted that 
(Mi) =f(O1) X1/Qa (207) 
Factors pertaining to constituent M, in tables 13 and 14 are based 
upon the above formulas. 
126. Because of the omission of the factor +/2.307 from formula 
(206), the node factors for M, which have been in general use since 
this system of tidal reductions was adopted are about 50 percent 
ereater than was originally intended, while the reciprocal reduction 
factors are correspondingly too small. This constituent is relatively 
unimportant and no practical difficulties have resulted from the omis- 
sion. The M, amplitudes as reduced from the observational data are 
comparable among themselves but should be increased by 50 percent 
to be on the same basis as the amplitudes of other constituents. The 
predicted tides have not been affected in the least since the node 
factors and reduction factors are reciprocal and compensating. The 
theoretical mean coefficient for this constituent with the factor +/2.307 
included is 0.0317; but in order that this coefficient may be adapted 
for use with the tabular node factors when computing tidal forces or 
the equilibrium height of the tide, the coefficient 0.0209 with the 
factor 2.307 excluded should be used. 
127. Although M, is one of the relatively unimportant constituents 
and the error in the node factor has caused no serious difficulties, it 
may be questionable whether it should be perpetuated. It is obvious, 
however, that any change in the present procedure would lead to much 
confusion unless undertaken by general agreement among all the 
principal organizations engaged in tidal work. By making any change 
applicable to the analysis of all series of observations beginning after 
a certain specified date it would be possible to interpret the results on 
the basis of the period covered by the observations without the neces- 
sity of revising all previously published amplitudes for this constituent. 
THE L2 TIDE 
128. The composite L, constituent is formed by combining terms 
A, and A, of formula (64). Neglecting the general coefficient and 
common latitude factor these terms may be written 
term A,,=1/2 e cos* J cos (2T—s+2h—p+180°+2&—2y) (208) 
term Ay=3/4 e sin? J cos (27—s+2h-+ p—2p) (209) 
A reference to table 2 will show that the mean coefficient of the first 
term is about four times as great as that of the latter term. The first . 
