ON THE HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 57 
Similarly, dé/dt is to be expressed in degrees, if « be in degrees. 
&/, P’ can be found for the antecedent moments, 57°°3 tan 2(«—p)/20, 
and 57°3 tan 2(u—v)/(*—7a), before the time r. 
§ 7. The Diurnal Tides. 
I shall not consider these tides so completely as the semidiurnal ones, 
although the method indicated would serve for an accurate discussion, if 
it be desired to make one. 
The important diurnal tides are K,, O, P. 
From Schedule B ii., 1883, we have 
sin I cos? 37 : 
0)=—S - 008 3 eM’ cos [t+h—v,—2(s—2)4+42—p']. 
(9) sin w cos? $w cos* $7 eatin’ GOs ed 
By (9) the coefficient is sin 2\/sin 24,, and we shall put, as in the 
case of the semidiurnal tides, 
Then, since +h=W+a, 
(0)=M,! cos [W+ (a+r) —2(s—8) +47] 
= M_!cos.O7 foe, brévityoe)\..- 7 e) . « & « Ge) 
Again, from Schedule C, 1883, 
(P)=S" eos ft—h+4n—2'} ; 
Then let y=2(s—h)+7,—2—¢’ +p’, and we have 
(Py=B8" cos (OF) ad ee etre AO) 
Whence 
(O)+(P)=[M,'+ 8’ cos x] cos Q—S’ sin x sin Q. 
If we put, 
H!' cos (p’—9')=M,'+ S’ cos x 
H! sin (p’—¢')=S’ sin x. 
(0) + (P)=H! cos (O+p'—9") 
=H cos [+ (a—v) —2(s—£) +47—9'] « (49) 
Where 
H'=/ {M,?2+ 8S? +2M,'8' cos x} 
S’ sin Bet ese Mra sh) 
and tan ('—9’)= Seve J 
P Be Gate M,'+ 8’ cos x 
The rate of increase of the angle y is twice the difference of the mean 
motions of the moon and sun, but it would be more correct to substitute 
for s and h the true longitudes of the bodies. It follows from (50) that 
¢’ has a fortnightly inequality like that of 9. 
{ is very nearly equal to 7’, and where the diurnal tide is not very large 
we may with sufficient approximation put 
(a—v,) —2(s—£)=—(s—5). 
So that with fair approximation 
(O)+(P)=H' cos [T—(s—é)+}r-9’/] . . . (51) 
