28 DISCUSSION OF TIDES IN BOSTON HARBOR. 
These values satisfy the conditions with an average residual of .025 foot and a maximum of 
06 foot. The residuals do not indicate any sensible term depending upon the angle 37 in the 
oscillations of the third kind, as may be also inferred from theory. 
With the preceding values (49) gives 
Ky Ry —— (059 ft., Ro, i) = 0.504, 40,1) = 0 
(63) K,R, =+ 0.681 ft, Rey = 0.1888,  ae1) ——10°29’ 
Ky Fp ——— 01023; ft.. Re, 10) —=— 0.0047, 42, 10) =— 20° 
These are the constants of two of the terms in the expression of A, and of one of the terms of 
Aoy (24). 
In obtaining the values of R from K R the values of Ky and Ky, (31) and (60), have been used. 
It will be remembered that R expresses the ratio of the inequality to the mean tide in each kind of 
oscillation. As the inequality Rei) of the second degree is scarcely sensible, it is not probable 
that there are sensible inequalities of the third degree. 
From (28) we get, expressing the value of a; in terms of the radius, 
183 14.60 
°6 
(64) 7 —= 21,03 — 
for the age of the tide from the heights. 
INEQUALITY DEPENDING UPON THE MOON’S MEAN ANOMALY. 
29. From the footings of Table III we get the following table of average values of all the 
observations contained within the limits of each of the twenty-four equal divisions of 72,in which the 
middle of the division is taken as the value of 7 belonging to the averages. In these footings the 
inequality depending upon (—y’) is eliminated, and they consequently contain only the inequality 
depending upon 7p: 
TABLE VI. 
Obs. Ne Ny Ne H, H’, 
h. m. h. m Feet. Feet. 
561 15 0 37.9 6 52.3 5. 894 4. 426 
546 30 0 39.0 6 53.6 5. 882 4. 378 
509 45 0 40.1 6 54.8 5. 850 4. 422 
552 60 0 40.8 6 56.0 5. 771 4. 554 
501 75 0 42.0 6 956.2 5. 566 4. 692 ji 
548 90 0 43.4 6 57.0 5. 376 4.917 
599 105 0 44.0 6 o7.1 5. 122 5. 112 
365 120 0 45.0 6 58.4 5. O15 9. 372 
ood 135 0 47.5 6 59.9 4. 854 5. 552 
553 150 0 47.8 6 59.5 4. 652 5, 692 
O46 165 0 48.3 6 53.9 4.515 5. 840 
530 180 0 48.7 6 59.5 4. 448 5. 966 
545 195 0 48.7 6 59.3 4. 374 6. 014 
559 210 0 47.5 6 58.4 4.379 6. 047 
547 225 0 45.8 6 56.7 4. 398 6. 025 
552 240 0 44.7 6 55.2 4. 406 5 953 
549 255 0 42.3 6 53.5 4. 502 5. 797 
556 270 0 40.3 6 51.6 4. 676 5. 630 
553 285 0 38.3 6 50.1 4. 840 5.510 
590 300 0 37.1 6 49.8 5. 045 5. 281 
5o4 315 0 35.9 6 49.0 95. 215 4. 992 
546 330 0 35.4 6 48.9 5. 408 4. 802 
556 345 0 35.7 6 49.4 5. 605 4. 593 
551 360 0 37.2 6 310 5. T12 4. 480 
13, 254 Means. 0 42.24 6 54.84 5. 068 5. 252 
From the footings of this table the constants of the mean tide might also be obtained, as in the 
preceding case, but they would not differ sensibly, as may be seen by comparing the footings of the — 
an 
