30 DISCUSSION OF TIDES IN BOSTON HARBOR. 
-TaBLe VII. 
Combined transits. The differences of transits. 
Obs. 
% Ay Ng Hy H’, (Ay re As) Qe— Na) (8, — Hg) (H,— Hy) 
® h.m. h.m. Ft. Ft. m. m™. Ft. Ft. 
555 7.5 0 41.7 6 53.4 5. 182 5. 123 +2.0 —2.8 |—0.486 | + 0.234 
553 22.5, 0 43.5 6 55.1 5. 148 5. 145 BD) 4.0 0. 719 0. 391 
555 37.5 0 44.8 6 57.95 5. 106 5. 233 3.4 4.7 0. 822 0. 481 
556 52.5 0 45.4 6 57.8 5. 043 5. 282 4.8 4.8 0. 886 0. 589 
347 67.5 0 44.2 6 57.0 4.991 5. 334 5.1 3.0 0. 992 0. 523 
548 82.5 0 42.5 6 55.2 4,998 5. 355 yal 5.4 0. 963 0. 636 
550 97.5 0 39.4 6 52.4 4.999 5. 365 5.0 4.3 0. 888 0. 540 
545 112.5 0 36.8 6 50.3 5. 029 5. 334 5.6 IEG) 0, 667 0. 482 
552 127.5 0 33.9 6 48.7 5. 024 5. 234 3.5 2.5 0. 567 0. 383 
558 142.5 0 36.5 6 49.1 5. 075 5.199 peal —2.2 |—0. 235 0. 160 
563 157.5 0 39.1 6 51.5 5. 122 5.178 24 +0.1 |+0.001 | + 0.042 
553 172.5 0 43.0 6 54.4 5.131 5. 168 +0.3 2.7 0.227 |—0. 068 
566 187.5 0 45.2 6 56.9 5.131 5.157 —2.0 2.8 0. 555 0. 230 
558 202.5 0 47.9 6 99.9 5. 086 5. 215 2.5 3.1 0. 739 0. 352 
563 217.5 0 49.1 6 61.9 5. 056 5. 291 3.8 4.1 0. 830 0. 501 
562 232.5 0 50.4 6 63.0 5. 015 5. 390 3.1 4.5 0. 942 0. 578 
563 247.5 0 49.6 6 62.0 5. 007 5. 434 4.0 5.5 0. 945 0. 576 
557 262.5 0 46.4 6 59.0 4. 997 5. 427 6.4 3.7 0. 872 0. 511 
552 277.5 0 43.5 6 56.5 4. 924 5. 403 4.2 | 5.1 0. 852 0.519 
541 292. 5 | 0 40.4 § 53.1 4.998 | 5. 304 3.9 2p} 0. 769 0. 479 
558 307.5 0 38.0 6 50.7 5. 056 5. 220 4.7 1% 0. 5382 0. 400 
545 322.5 0 36.5 6 49.4 5.101 5. 136 2.3 +01 0. 328 0. 206 
569 337. 5 0 37.4 6 50.3 5. 168 5. 097 1.6 —1.6 |+4 0.042 |—0,115 
546 352. 5 0 39.2 6 51.0 5. 203 5. O71 —1.5 |e 3.9 | —0.291 | + 0.081 
Means. 0 42.35 6 54.83 5. 067 9. 295 | 
The inequalities in the values in the preceding table are affected by the tide produced by the 
small term in the moon’s disturbing force depending upon the fourth power of the moon’s distance. 
The expression of this tide, and also of the lunitidal interval, contains the angle ¢, (33); and hence 
the expressions representing the inequalities in the preceding tabular values must contain such an 
angle. By proceeding in the same manner as in the preceding cases, we obtain from the preceding 
table forty-eight equations of the form, 
6L—M" sin g+N” cos ¢+M; sin 43+N; Cos 75 
These equations give 
M”=—2™.1, N’——1™.4, Neo N;==(0".5 
From these we get by (48), 
Oe, e// —__ 3.40 
(62) B, =5".3, ass we 
These constants satisfy the conditions, with an average residual of 0™.4 and a maximum of 1™.4. 
From the values of H’; and H’, inthe preceding table we obtain, as in the preceding cases, from 
(50) forty-eight equations of the form 
6 H= Ky (Mz; cos 734 N3 sin 73) + Ky (Ms; cos 73+N; sin 73+ M” cos g+N sin ¢ 
From these forty-eight conditions we obtain 
K,M;—=—.021 ft., K, Ms = + .107 ft., M” = + .030 
Ky No>=+ .005 ft., K, N;=—.012 ft., NY — + .007 
With these values (49) gives 
Ky R; === 022 ft., Ro, 3)—.190 Zo, 3) =—149 
(70) K, R; = 109 ft., Re. 3) .0225 2233) ———— 6° 30! 
K, R’= 032 ft., R” =.0065 al! = ==-++ 13° 
