26 DISCUSSION OF TIDES IN BOSTON HARBOR. 
THE CONSTANT OR MEAN TIDE. 
27. From the footings of Tables I and II we get the following table of average values of all the 
observations contained within certain limits of the argument (— wv’), and corresponding to the given 
average of the argument. These values, consequently, are independent of the effects depending 
upon any of the other arguments, and their inequalities depend only upon the argument (~—v’), 
TABLE Y. 
i 
UPPER TRANSITS. LOWER TRANSITS. COMBINED TRANSITS. 
Obs.| (W—w’)| A » | Obs.) (YW) | As As Hz, | Hy | Obs.| (W—wW)) Ay Ne) ee 
| f | | 
h. ™. ln. m. \h. m. | re | hom. |h. m. Vey | me) me hom. |hom. |hom | Fe | Ft 
273 | 015.2 | 0 40.3 | 6 50.3 | 5.63 277 | 015.7 | 0 40.4 | 6 50.8 | 5.64 | 4.62} 550) 015.4] 0 40.3} 650.5] 5.63] 4.60 
275 | 0 44:8 | 0 34.6 | 6 44.5 | 5.51 275 | 0 45.2} 035.1) 6 45.9) 5.59) 4.69] 550| 0 45.0) 0348)6 45.2) 5.55] 4.70 
964 | 114.4 | 0 30.9 | 6 41.4 | 5.46 263 | 114.7] 030.6 | 6 42.3) 5.46] 4.84] 527] 114.6/030.8|/6 41.8) 5.46] 4.78 
985 | 1 44.4 | 0 26.4 | 6 37.4 | 5.31 274 | 144.8 | 027.1) 637.9] 5.36 | 4.94] 559] 1446/|026.7/637.6] 5.33] 4.95 
283 | 215.6 | 0 23.9 | 6 34.4 | 5.20 279| 214.6|0228)6340/5.14| 5.17] 562} 2151/]0234/6342] 5.17] 5.18 
269 | 2 44.6 | 0 20.7) 6 32.4 | 5.05 268 | 2 44.6 | 0 21.3 | 6 33.4 | 5.09] 5.33] 537] 2 44.6] 021.0] 6329] 5.07] 5.32 
a0 | 315.8) 019.8] 6 31.8 | 4.92 295 | 314.5] 019.4] 6.31.4] 4.891555] 565) 315.2/019.6|6 31.6] 4.90] 5.55 
280 | 3 44.2 | 0 20.3) 6 326) 4.74 281 | 3 45.6 0 20.3}6339/4.74|5.73] 561| 3449/020.3]6 33.2] 4.74] 5.72 
283 | 415.9 | 0 23.2 | 6 36.7 | 4.58 283} 414.8/0226|6 36.3) 4.58] 5.81] 566] 415.3)0229|]6365| 4.58] 5.85 
983 | 444.8 026.4 | 6 40.0 | 4.50 272) 445.8] 0 27.6 | 6 42.2] 4.48] 5.99] 555) 445.3) 027.0) 641.1] 4.49] 5.95 
983 | 515.6 | 0 32.3 | 6 47.8 | 4.48 273 | 514.3] 032.0] 6 47.2) 4.48) 5.99] 556] 515.0} 0321)647.5| 4.48] 5.98 
988 | 5 44.3 | 037.9 | 6 52.8 | 4.46 am | 5 45.0] 039.1} 653.8) 4.39| 6.00] 559) 5 44.7|/0385|653.3| 4.43] 6.03 
976 | 615.5 | 045.9) 7 0.9 | 4.46 291} 614.0] 0 44.6|7 0.2) 4.47] 5.96] 567| 614.7) 045.3|7 0.6] 4.46] 6.00 
283 | 6 44.2) 050.8|7 6.3 | 4.54 289) 6 46.0)0526)7 7.0) 4.51])5.85] 572) 6 45.1)051.7|7 66| 4.52) 5.82 
271 715.4 | 058.4 713.1 | 4. 62. eg | 714.8|056.4|711.6/ 4.64] 5.55] 549| 715.1] 0574/7124] 463] 5.63 
984] 7442/1 1.0) 7161) 4.84 273 | 745.2)1 25/7170) 4.81)5.52) 557] 7447)1 17/7165) 4.82] 5.50 
281] 8 15.8/1 5.9] 718.6 | 4.87 287) 814.6) 1 4.6) 717.5) 4.95) 5.31] 568) 815.2)1 5.3) 7180) 491) 5.32 
980] 8 44.5)1 4.8) 717.1 | 5.22 275 | 845.9)1 5.4| 718.2) 5.06]5.10] 555] 845.2]/1 51/7176) 5.14] 5.08 
282] 9152/1 4.8) 7 16.2 | 5.21 272) 915.5/1 3.6) 7165] 5.34] 4.90} 554] 915.3/1 42/7163) 5.27] 4.92 
276) 9449/1 1.5) 7129 | 5.49 268} 945.4]/1 26/713.8| 5.42] 4.88] 544] 945.1]/1 20/7133] 5.46] 4.83 
$75 | 1015.0 | 059.1|7 9.8 | 5.50 276 | 1014.7] 057.4) 7 9.7) 5.61) 4.671 551] 10149|0582]/7 9.8] 5.55) 4.73 
980} 10 44.3/053.7|7 4.3 | 5.72 264| 10 45.5) 0538) 7 4.8) 5.59| 464] 544| 1044.9] 0537/7 4.5] 5.66] 4.61 
78 | 11 15.3 | 0 49.0 | 6 59.7 | 5.68 280 | 1115.1 | 0 47.2| 6 59.8 | 5.68] 4.55} 558) 1115.2) 048.1] 6 59.7] 5.68] 4.53 
268 | 11 45.1 | 0 45.4 | 6 55.3 | 5.67 269 | 11 45.7 0 44.2| 6 54.8 | 5.68 | 4.50 537 | 11 44.7 | 0 44.8} 655.0] 5.67] 4.54 
Means...) 0 42.37] 6 54 67 5.070 | Means..| 0 42. 2 6 55.00] 5.062) 5. 257] Means..| 0 42.29| 6 54.24/ 5.066| 5.257 
| 
In the footings of this table the inequalities having the argument (~—¥v’) are also eliminated, 
and we have results belonging to the mean tide. Since the diurnal tide depends upon g, it is also 
eliminated, and we have left only the constant part of the other oscillations. 
With the preceding mean values of 4’; and 4’, we get from (44), supplying the omitted constant 
of 2 days, 
(56) Bo = 4 (2% 0" 42™,294 24 6b 54™.84 — Gh 12™,62) — 24 Ob 42™,25 
which is the mean establishment of the port belonging to the assumed transit. In order to reduce 
this to the transit immediately preceding high water, we must add the constant part of k (34), put- 
ting n=3, and we thus get 
Bo= 2? 08 42™.25 — 1¢ 132 13™,.14 = 02 115 267.53 
From the first of (37) we get, since L.—=B, in this case, 
9 
Q2=6 54.67 —0 42.25 —142— 07.20 
Sq@=0 42.22—0 42.2 
Gs—=6 55.00 — 0 42.25 = $2407.13 
in which z=12 lunar hours or 12" 25™.24 in solar time. Hence all the intervals between high and low 
and low and high waters in the mean tide are almost exactly one-fourth of a lunar day. 
(57) 
