78 U. S. COAST AND GEODETIC SURVEY 
place and the theoretical time as determined by the equilibrium 
theory. The distance from the beginning of the series to the follow- 
ing high water is the ¢ of formula (300), which is determined directly 
from the analysis of the observations. From the figure it is evident 
that the x is the sum of (V,+4) and ¢, and also that it is independent 
of the time of the beginning of the series. 
228. Figure 8 gives a more detailed representation of the epoch of a 
constituent. In this figure the horizontal line represents changes in 
time. Distances along this line will be proportional to the changes 
in the angle of any single constituent, but since each constituent 
has a different speed equal distances along this line will not represent 
equal angles for different constituents. The time between the events 
may be converted into an equivalent constituent angle by multiplying 
by the speed of the constituent. The figure is to some extent self- 
explanatory. The word “‘transit”’ signifies the transit of the fictitious 
moon representing any constituent and also the time when the equili- 
brium argument of that constituent has a zero value. For all short- 
period constituents the time of such zero value will depend upon the 
longitude of the place of observation as well as upon absolute time. 
For long-period constituents the zero values are independent of the 
longitude of the place of observation, and the ‘‘transits’’ over the 
several meridians may be considered as occurring simultaneously, 
which is equivalent to taking the coefficient p equal to zero. The 
figure illustrates the relation between the Greenwich (V,+w) calcu- 
lated for the meridian of Greenwich and referring to standard Green- 
wich time and local (V,+) referring to the meridian of observation 
and the actual time of the beginning of the observations. 
INFERENCE OF CONSTANTS \ 
229. Under the conditions assumed for the equilibrium theory the 
amplitudes of the constituents could be computed directly by means 
of the coefficient formulas without the necessity of securing tidal 
observations, and the phases would correspond with the equilibrium 
arguments of the constituents. Under the conditions that actually 
exist it has been found from observations that the amplitudes of the 
constituents of a similar type at any place, although differing greatly 
from their theoretical values, have a relation that, in genera], agrees 
fairly closely with the relations of their theoretical coefficients. It 
has also been ascertained from the results obtained from observations 
that the difference in the epochs or lags of the constituents have a 
relation conforming, in general, with the relation of the differences 
in their speeds. This last relation is based upon an assumption that 
the ages of the inequalities due to the disturbing influence of other 
constituents of a similar type are equal when expressed in time. 
230. If the mean amplitudes, epochs, and speeds of several constit- 
uents A, B, C, are represented by H(A), H(B), H(C), x(A), «(B), 
«(C), and a, 6, c, respectively, the above relations may be expressed 
by the following formulas: 
mean coefficient of P 
mean coefficient of AHA) (322) 
eG) — 
