ON THE HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 47 
Tn all the smaller tides we may write 
t+h—s—(»,—f)=yv. 
A general formula of transformation will be required below. Thus, if 
cos 2a= X, sin2x—X’, 
cos 2(p=a—a)=(X= tan2(a—p)X’) cos2(~—a) 
xe . 
es a a eo 9 fa & 4 
cos an ie 20/—n) (17) 
The lunar K, tide. 
From Sched. B. i., 1883, we have 
m2 
Lunar K,=~ es ES ee eee 
sin?m(1—3sin?/) 
sin?A ; 
= sat cos2[w+ (s—£)—«]. 
Applying (17) with X=D, X’=D’', a=x, and taking the lower sign, 
ot 
eae K,— = er] (D+ tan 2(«— p)D') cos2(b—«) 
/ 
,sin (bp) J. IK a) 
~ 60s 2(k—pe 
/ 
In the case of the sun we neglect the terms in D’, for the same reasons 
as were assigned for the similar neglect in (16), and have 
Solar K,=K/"D,cos2(f,—x) » . . 2). . (19) 
The tide N. A 
From Schedule B.1., Report 1883, 
(N= 0083! _ Neos [2(t-+-h—s— 1, +2) —(s—p) —201, 
7 
cost $weos*4 
Then (N) = 22°" Neos2[¥—y—F(s—p)]. 
cos?A, 
_ Then applying (17) with X=II, X’=Il’, a=», and taking the upper 
sign, but writing »—v instead of »—p, because this tide being slower 
than M, suffers less retardation, 
(N)= = Nf a + tan 2(p—7)II’) cos2(p— v) 
os?A, 
It’ P 
+ SeBqecay sin 2—w) | (20) 
The tide L. 
We shall here omit the small tide of speed 2y—c+a, by which the 
true elliptic tide is perturbed. ‘Thus the F# in the column of arguments 
in Sched. B. i., 1883, is neglected, and we have 
41 
(L)=— BLS 7 Le re PER eres +(s—p)—2)] 
cos*Sw cost 47 
_ __c¢os?A ad Ser a 
= can cone? A+4(s—p)]. 
