HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 59 
one year, and this period is not long enough to distinguish completely 
a tide whose argument is 2y—o,—za,, from one whose argument is 
2x—0,+7,, nor one whose argument is y—c,—a,, from one whose argu- 
ment is x—7,+a, In fact, the tide with argument 2y—«0,+<, (for 
which no analysis has been as yet carried out) will only produce an 
irregularity in that of argument 2y—«,—z,, called the smaller elliptic 
semidiurnal tide ; such irregularity has in fact been noted, but no expla- 
nation has previously been given of it. 
Again, the pair of terms with arguments y—c,+-, will appear in the 
harmonic analysis with the single argument y—<,, and the resulting 
numbers will necessarily appear very irregular, unless compared with the 
theoretical expression (20), 
We will now consider the terms introduced by the two principal lunar 
ineqnalities due to the disturbing action of the sun. 
The Evection. 
Let 6 be the moon’s longitude in the ecliptic. 
s the moon’s mean longitude. 
p the mean longitude of the perigee.? 
h the sun’s mean longitude. 
m the ratio of the sun’s to the moon’s mean motion. 
Then that inequality in longitude and radius vector is represented by 
O=s+lPmesin(s—2h+p) . .. . . (21) 
ee 
AB cn La a hs 3g me Cos (@—2h-+p) -. «ss 5.22) 
= 
If we neglect the distinction between longitudes in the orbit and in 
the ecliptic [which is in effect neglecting a term with coefficient 
sin? (+x 5° 9’) ], we have from (21), 
l=o,+1?me cos (s—2h+p) ; 
whence 
cos (21-+a)=cos (20, +a) +13 me [cos (2c,+s—2h+p+a) 
—cos (26,—s+2h—p+a) ] 
And from (22) and the definitions of R, ¥, ® in (11), 
—¢2)73 
ered =1+ 43me cos (s—2h+p) width Sb cal yan hy Coen) 
¥(a)=cos a+4%me [cos (s—2h+p+a)+cos (s—2h+p—a)] . . (24) 
® (a)=cos (20,44) +195 me cos (20,+s—2h+p+a) 
—tYeme cos (2eo,—s+2h—pta) . . (25) 
Then substituting from (23), (24), (25), in (12), and dropping the 
(tp in’ this sense will easily be distinguished from the p used to denote cos 3 7, 
which latter will, moreover, be shortly discarded. 
