HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 83 
Suppose, then, that P be the longitude of the perigee at mid-year, 
measured from the intersection, and that we compute I? from the formula 
ey 
sin 2P (52) 
tan R= = = 
+ cot? 5 I— cos 2P 
Then the treatment will be the same as in all the other cases, if the 
argument V+w be taken as 2/+2(h—») —2(s—f£)+(s—p)—R+7. 
The factor f in this case is equal to 
cost 4 I A 
ets {1—12 tan? 4I cos 2P}. 
The Tide M,. 
Reference to schedule B (ii.) shows that this tide must be propor- 
tional to 
exsinIcos*5 IV {$+ $cos2(p—£)} x cos[¢+(h—v) —(s—£) + Q—4$2 ] (52) 
© 
a 
where tan Q=4 tan (p—£). 
We must here deem Q to form a part of the function wu, for which a 
mean value is to be taken ; but as in the case of the L tide, this course is 
not very satisfactory. 
If P as before denotes the longitude of the perigee at mid-year, 
measured from the intersection, and Q be computed from 
panG 2 tan Po yb. 5 shot datedmie atooe) 
then the argument V+ will be 
t+(h—v)—(s—£)+Q—4r. 
And the factor f is 
sin I cos? 41 . 
: sa ar V (3 +3 cos 2P} » Un eresiiGast’) 
sin w cos? dw cos! $7 
It has been shown that the tide M,, in as far as it depends on the 
fourth power of the moon’s parallax, is too small to be worth including 
in the numerical analysis. 
§ 6. On the Method of Computing the Arguments and Coefficients. 
Ty performing the reductions of the preceding sections a number of 
numerical quantities are required, which are to be derived from the 
position of the heavenly bodies. 
Formule for Computing I, v, &. 
From Fig, 2, § 3, we see that 
cot (N—£) sin N=cos N cos i+sin i cot w 
cot vy sin N=cos N cos w+sin cot ¢ 
cos I=cos i cos w—sin / sin w cos N 
If 3 be an auxiliary angle defined by 
ieme—tan t cos Noh yy ous eb oa eet (54) 
G 2 
