HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 65 
p, v,& In B, i. 244+ (2h—2r), and in B, ii. ¢+(h—v), are common to all 
the arguments, and they are written at the top of the column of arguments. 
The arguments are grouped in a manner convenient for subsequent 
computations. 
Fourthly, there is a column of speeds, being the hourly increase of 
the arguments in the preceding column, the numerical values of which 
are added in a last column. 
Every term is indicated by the initial letters (see § 1) adopted for the 
tide to which it corresponds, except in the case of certain unimportant 
terms to which no initials have been appropriated. 
To write down any term: take the general coefficient; the coefficient 
for the class of tides; the special coefficient, and multiply by the cosine 
of the argument. The result is a term in the equilibrium tide (with 
water covering the whole earth). The transition to the actual case by 
the introduction of a factor and a delay of phase (to be derived from 
observation) has been already explained. 
The solar tides. 
The expression for the tides depending on the sun may be written 
down at once by symmetry. The eccentricity of the solar orbit is so 
small, being ‘01679, that the elliptic tides may be omitted, excepting the 
larger elliptic semi-diurnal tide. 
The Innar schedule is to be transformed by putting s=h, p=p,, 
f=rv=0, o=n, I=w, e=e,, w=. In order that the comparison 
of the importance of the solar tides with the lunar may be complete, the 
3 
same general coefficient 25 (*) a will be retained, and the special 
c 
5 
coefficient for each term will be made to involve the factor 7,/7. Here 
3 - S being the sun’s mass. 
With #/M=81 5, 
71 46085 =>. 
The schedule [C] of solar tides is given on page 21. 
The subsequent ‘schedules [D] and [E] give all the tides of purely 
astronomical origin contained in the previous developments, arranged 
first in order of speed, and secondly in order of the magnitude of the 
coefficient. As most of the observations of the tides are made at places 
remote from the pole, the coefficients of the tides of long period are 
written down with a general coefficient 1—3 sin?/ in place of 4—3 sin/: 
that is to say, the spherical harmonic function has the value unity at the 
equator and two at the pole. In schedule [KE] the tides K,, K, originate 
both from the moon and sun, but the lunar and solar parts are also 
entered separately. 
The coefficients of the evectional and variational tides are computed 
from the full values to those inequalities. 
In the schedule [E] the tides are marked which occur in the ‘ Tide- 
predicter’ of the Indian Government in its present condition. 
1883. F 
