DISCUSSION OF TIDES IN BOSTON HARBOR. 35 
The preceding twenty-four equations of conditions also give 4—31°. Expressing this value 
in solar time, we get from (37) L.—L,—2" 8™ for the time the high water of the diurnal tide precedes 
that of the semi-diurnal tide. 
We consequently have 
(82) Bo = 2? 08 49m — 2h Gm — 14 29h 34m 
for the mean establishment of the diurnal tide belonging to transit C. 
It is evident from (41) that $(2; — 23) =q@ and 4(4.—/,) =42—q. With the preceding values 
of K; and 4, and Ky (60), we get from (55), expressing ares in time, 
a=+ 1.8 sin (g—a) 
$z— @—=— 3.0 sin (g — a) 
in which a must have the value above. Hence these expressions should represent 4(2;—A;) and 
$(42—2,) in Table VII. The angle of the epoch is about right, but the coefficient of the former is 
nearly one minute too small and that of the latter a little too great. These slight discrepancies are, 
no doubt, caused by the existence of a small quarter-day tide, which has not been taken into account 
in (41), from which the preceding expressions have been deduced. 
RECAPITULATION OF RESULTS. 
35. For the general tidal expressions, (24) and (26), the following constants have been obtained, 
in which the values of the epochs are for transit C: 
In oscillations of mean level, in which s—0, 
pS OA Rie, 
Ri= 0.504, q== . @ 
R= 0.308, et 
(3) R;= 0.190, a;—=— 14 
R.= 1.08, y= 4 
Rs —! 0:62) ds = — 82 
In diurnal oscillations, in which s—1, (32), 
(84) KG OF Sitiies a—=— 199.7, Bo= 14 220 34™ 
In semi-diurnal oscillations, in which s—=2, 
K,= 4.904 ft., Bo = 22 02 497.25, 
R, = (0.1888, a, —=—10°.5, B, =— 22".6, ec 0° 
Ro = 0.1624, d =—+ 22.7, By =. O82 & == 459.6 
R3; = 0.0225, C= OSs) 5 = TAs S= 
R, =— 0.0077, a, =— 65°, B, =— 3™9) &4 =— 713° 
(35) <R; =—0.0019, a; =—58°, B; =— 0"6, «© =—10° 
\Re =— 0.0235, ag =—119, Bs =— 2.5,  « =—50° 
R, = 0.0054, ag =—459, = Is £3 —=— 250 
Ry = 0.0240, a —=— 219, By = =H QS We 
Rypy=— 0.0045, 239 = — 29, Bio = BD ; €10 = 5° 
Ry= 0.0107, a = — 99; i OS ey — 77° 
In tertio-diurnal oscillations, in which s—3, 
(86) K,= 0.004 ft. : 
In the semi-diurnal tide, depending upon the fourth power of the moon’s distance, (36), 
(87) K” =.0065, al! — 77°, ye BE IS 
The absolute values of the coefficients of the tide are K, R;. 
COMPARISONS WITH THE EQUILIBRIUM THEORY. 
36. The values of the constants K, in the equilibrium theory, and also in the dynamic theory in 
the oscillations of mean level, are given approximately in (31). By comparing these values with 
