TIDAL OBSERVATIONS. 491 
constituents may be called for brevity elliptic and declinational tides. But 
two of the solar elliptic diurnal tides thus indicated have the same period, 
being twenty-four mean solar hours. Thus we have in all twenty-three tidal 
constituents :— 
Coefficients of ¢ in arguments. 
Lunar. » Solar. 
The lunar monthly and solar annual (elliptic). 2 o n 
The lunar fortnightly and solar semiannual| 5 9 2 
(declinational) 7 a n 
The lunar and solar diurnal (declinational) . 4 { Y &. ¢ 
y—20 | y—2n 
The lunar and solar semidiurnal ~2 2(y—e) 2(y—n) 
Vee fy on 
The lunar and solar elliptic diurnal oe fre Pei), Yont 
Pts ||) Yak 
y—3e0+a y—3n 
ry 5 hen peer 2y— o—@D 2y- qn 
The lunar and solar elliptic semidiurnal. . 4 { Ay i | a 
The lunar and solar declinational semi- 
: 2 ay 2Qy 
diurnal pbk dine eth, as 
3. Here y denotes the angular velocity of the earth’s rotation, and o, n, a 
those of the moon’s revolution round the earth, of the earth’s round the sun, 
and of the progression of the moon’s perigee. The motion of the first point 
of Aries, and of the earth’s perihelion, are neglected. It is almost certain 
that the slow variation of the lunar declinational fides due to the retrogres- 
sion of the nodes of the moon’s orbit, may be dealt with with sufficient 
accuracy according to the equilibrium method; and the inequalities produced 
by the perturbations of the moon’s motion are probably insensible. But 
each one of the twenty-three tides enumerated above is certainly sensible 
on our coasts. And there are besides, as Laplace has shown, very sensible 
tides depending on the fourth power of the moon’s parallax*, the inves- 
tigation of which must be included in the complete analysis now sug- 
gested, although for simplicity they have been left out of the preceding 
schedule. The amplitude and the epoch of each tidal constituent for any 
part of the sea is to be determined by observation, and cannot be determined 
except by observation. But it is to be remarked that the period of one of 
_ the lunar diurnal tides agrees with that of one of the solar diurnal tides, 
being twenty-four sidereal hours; and that the period of one of the semi- 
_ diurnal lunar declinational tides agrees with that of one of the semidiurnal 
solar declinational tides, being twelve sidereal hours. Also that the angular 
velocities y—o+a@ and y—o—q@ are so nearly equal, that observations 
through several years must be combined to distinguish the two corre- 
sponding elliptic diurnal tides. Thus the whole number of constituents to 
be determined by one year’s observation is twenty. The forty constants 
Specifying these twenty constituents are probably each determinable, with 
considerable accuracy, from the data afforded in the course of a year by a 
good self-registering tide-gauge, or from accurate personal observations taken 
at equal short intervals of time, hourly for instance. ach lunar declina- 
tional tide varies from a minimum to a maximum, and back to a minimum, 
———_e 
; [* The chief effect of this at any one station is a ¢er-diwrnal lunar tide, or one whose 
iod is eight lunar hours. A probable indication of this has been obtained from the 
msgate tidal diagrams of 1864. See § 22 below.] 
242 
