6 DISCUSSION OF TIDES IN BOSTON HARBOR. 
We shall also put, for the mean values of r and 7’, 
Z, _ 3H 
4 ys 
3p! 
(8) Caer: 
UH ] 
e=— 
Z 
If we put, in terms of the earth’s mass, 
(9) p=.0138+0 4 
in which 6p is the correction of the assumed mass of the moon, we shall have 
(10) €= 4380 — 33.8 0 p 
9. With the preceding constants and notation, when s—0, (7) gives : 
(11) 2Qo—= Cy 5; P; cos 7; 
in which, omitting the correction of the moon’s mass, 
Co=  .254 (1—3 cos? 0)(1+¢) Z 
P, 114, 42=” 
(12) Pee ie 73==2 9 
7 OG 74—! 
Pe 09o% Is—=2 ¢! 
Pp=— .025, 16—= 0 
The term belonging to 11, in this case, is wanting. 
10. When s=1, the development of the resultant of the moon and sun in the general form of 
(7) is not sufficiently convergent for practical purposes, and therefore expressions must be obtained 
for the moon and sun separately in this case. The only terms, in the case of the moon, which we 
shall have occasion to use in this discussion, may be most conveniently expressed in the following 
form, # vanishing in this case : 
(13) 2;—=C;, sin ¢g cos (nt-+a— 1) 
in which 
(14) 1=.181 sin 2 6Z 
In the case of the sun we shall likewise have 
(15) 2,—=C%, sin ¢! cos (nt-+-a— »’) : 
in which 
(16) C’, =.731 e sin 2 0Z 
11. When s=2, (7) gives 
(17) 2,—=C, ¥, P; cos 7; cos 2 (n t-+a — y+ fr) 
in which 
C,= .9564V1+2@ sin? 0 Z 
Pi, = 4305 — 24.0 6 p, My =2 (vp — yp’), Dim —.426 
P,= 15214 3606p, 12 =, Di 42 = .229 
P; = 0985+ 1.06p, 13 =29, D; 73 = .460 
1, = .0093— 1.0 D pty N4 — ie 
(18) P; = .0053— 1.00p, 75 =2 9", 
Ps =—.0375, 76 =, 
Pa Oalo; 77 =29—v, Di 47 =-462 
Pe 008d; 73 = + 7, Di 73 = .655 
Py = _ .0085, 79 =11— Ney Di 79 —.197 
Py=— 0470 4+ 4.70, 710 == 2 1, Di G10 852 
The unit of time in the preceding derivatives is one solar day. 
12. When s=—3, (7) gives only one term producing any sensible effect upon the tides, which may 
be expressed by 
(19) 2;—=C; Cos 3 (nt-+-o—/) 
in which 
(20) C;=.0146 sin’ 0Z 
