54 REPORT—1885. 
Definition of symbols :— 
a, 6, a, 6, )’s and ©’s R.A. and declination at moon’s transit ; 
A=a—a,, apparent time of )’s transit at the port. 
ay Stan 8(k—p)s 
c’ )’sdecl. atthe time (generally earlier than transit)7 — 9 
o 
P, P, the ratio of )’s and ©’s parallax to mean parallaxes. 
P' the ratio for ) at the time (generally earlier than transit) 
™ 5703 tan 2(—v). 
C 
aa 
7 the time elapsed since )’s transit in m.s. hours; T the same time 
reduced to angle at 14°-49 per hour. 
A such a declination that cos? A is the mean value of cos?6; A has a 
13-yearly period. 
A, such a declination that cos? 4, is the mean value of cos? ¢,. 
e, e, eccentricities of lunar and solar orbits; « the )’s mean motion; 
e the mean motion of the )’s perigee. 
M. NN; Db, contsa 
MeN LL. cost Ay 
M, 8, Ky, N, L, T, R the mean semi-ranges H of the tides of those 
denominations in the harmonic method. The retardations found by 
harmonic analysis are 2 for M,, 2¢ for S., 2« for Ky, 2v for N, 2d for L, 
and 2¢ for T and R. ° 
N sin 2v—D, sin 2X 
Sin =" — Sin * 96 to be taken in the same quadrant 
N cos 2v—L cos 20’ : 
Lastly tan 2e= 
as 2, 
§ 5. Synthesis of the Several Terms. 
Consider the two principal terms in Schedule IV. 
M, cos 2(T—p) +S cos 2(T4+ A—Z). 
They may be written in the form 
H cos 2(T—9¢), 
where H cos 2(u—)=M, +S cos 2(A—f+4+p), 
H sin 2(u—)=S sin 2(A—f4+p). 
If we compute ¢ corresponding to the time of moon’s transit from the 
formula 
S sin 2(A—f+p) 
M,+Scos2(A—f+p)’ 
then » reduced to time at the rate of 14°49 per hour is the interval 
after moon’s transit to high water, to a first approximation. The 
angle ¢+90°, similarly reduced, gives the low waters before and after the 
high water, and ¢+180° gives another high water. The high waters 
and low waters are to be referred to the nearest transit of the moon. 
The height or depression is given to a first approximation by 
H=J/(M,?+8?+2M,S cos 2 (u—9)). 
tan 2(u—9) = 
