44. DISCUSSION OF TIDES IN BOSTON HARBOR. 
observation (56), and the inequalities are determined by (27) omitting Q, and using the preceding 
values of P; (94) belonging to the lunar tide only. This gives for the lunar part, 
(103) M,=1".7, M,=5™8, M;—6™1, &e. 
The first of these belongs to the small term in the moon’s parallax depending upon variation, and 
is added to the value of the first inequality depending upon f’, which is —24™.2, to give the 
whole semi-monthly inequality —22™.5. The second is the whole value of B,, there being no part 
depending upon f/’. The part of the third inequality depending upon #’ is —1™.0, and hence the 
whole value of B; is 5™.1. 
48. For the sake of convenience in computation we can put in (27),in the case of the lunar tide, 
(104) »; M; sin 75=C D; p+C/ sin 2 v Di v 
in which 
D; p=the hourly change of parallax in seconds, 
D,v=the change of declination in seconds for one minute of time. 
For the principal term of parallax of which the coefficient is 186.5; the hourly change is 
1.79 sin 72; also, the change of sin 2 v D; v inseconds for one minute of time is 5.6 sin 73. Hence, 
the constants in the preceding expression are determined by the following conditions, using 5".3 
given by observation for the value of M; instead of 5".8 given by theory, (103): ‘ 
= 1.79 C =52.3 
ee) } 5.6 O'=6,1 
These conditions give C=3 very nearly, and C’=1.1. With these constants, (104), using see- 
onds of are as minutes of time, gives the sum of all the terms depending upon D, 7;, independently 
of any developed expression, directly from the hourly differences of parallax, and the differences of 
declination for one minute, taken from the Nautical Almanac. : 
In addition to the preceding we have the terms 3; N; cos 7; (27) depending upon friction and 
other disturbing causes, of which it is only necessary to take account of the following, in which the 
coefficients given by observation are used, being reduced from transit D to the transit occurring at 
the time zr before the time of the tide, using the correction (34) for changing from one transit to 
another : 
Ny, cos 7;= 4.0 cos 7, 
Nz Cos 72—=— 6™.0 cos 72 
N; CoS 73= 1.5 cos 73 
N, cos 7x—= + 4.0 Cos 74 
Ng COS 7s—= +  2™.5 COS 75 
All the other terms of this form are included in the terms depending upon / in (99). 
The first three and the last of these terms are embraced in Table III, the fourth one in Table II. 
To both the times and heights must be added, also, the effect of the term depending upon the 
fourth power of the moon’s distance, given in (69) and (70). These inequalities are given in the last 
two columns of Table IV. 
The summation of the preceding effects gives the values of A», (24) or (33), and Ip, (26), 
The value of Ho, the height of mean level, neglecting the very small inequalities given by 
observation as of no practical importance, is given in Table III. 
The value of A, added to Hy, gives the height of high water, and, subtracted from Hy, gives 
that of low water. 
To both the heights and times must then be added the effects of the lunar and solar diurnal 
tides to obtain the complete height and time of the tide. The effects of the lunar tide upon both 
the height and time of the tide are contained in Table IV, and those of the solar diurnal tide in 
Tables VUI, IX, X, and XI. 
COMPUTATION OF A TIDAL EPHEMERIS. 
49, The method of using the preceding formule and results in the computation of a tidal 
ephemeris is most conveniently explained by a reference to the example given at the end: 
