ON THE HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 55 
This variability in the time and height of high water, due to variability 
of #, is called the “fortnightly or semi-menstrual inequality i in the height 
and interval. The period (¢—,)/(¢—7) is called ‘the age of the tide,’ 
because this is the mean period after new and full moon before the 
occurrence of spring tide. 
§ 6. Corrections. 
The smaller terms in Schedule IV. may be regarded as inequalities in 
the principal terms. They are of several types. Consider a term 
B cos 2(T—)3). 
Then 
B cos 2(T—)=B cos 2(3—¢) cos 2(T—¢) +B sin 2(3—¢) sin 2(T—¢). 
Hence the addition of such a term to Hcos2(T—@¢) gives us 
(H+6H) cos 2(T—¢—éo), where 
cH=B cos 2(B—¢), 2Hég~=Bsin2(B—¢). . . . (85) 
Next consider a term Csin2(T—p). Putting 6=y+47, we have 
cH=—Csin2(u—¢), 2Hég¢=C cos 2(u—) . . . (36) 
Next consider a term cos 2(T+A—Z). Putting B=f—A, we have 
cH=E cos 2(A—f+6), 2H¢¢=—H sin2(A—f+9) . . (37) 
4 Lastly, consider a term F’sin 2(T+A—Z). Putting b={—A-+41, we 
a éH=F' sin2(A—f+ 6), 2H¢g=F cos2(A—f4+¢) . . (88) 
In writing down the corrections we substitute 14°49é¢ for ¢9, and 
introduce a factor so that the times may be given in mean solar hours and 
the angular velocities in degrees per hour. 
Change of Moon’s R.A., Sched, IV. 
This is of type (36), and gives 
ieee et (ao ) 7M, Sie Cpa) 
180\de (39) 
seie977.27 (24 _ 4) Mo cos (u—$) | 
; 180 & ) a eae ) 
This correction to the height is very small. 
Change of Sun’s R.A., Sched. 1V.* 
This is of type (38), and gives 
ise ia? “ays sin 2(A—£+4) 
(40) 
or da 
nays 7 A= 
ct=—15-977 Tap (o- a) re 7 7 008 2(A—¢+¢) 
* With the value of A suggested in footnote to (32) («—da,/dt)r becomes 
{(¢—1)o—(eda, |dt—pn)] | (y—c) at high water. This is obviously very small. 
