TIDAL OBSERVATIONS. 509 
37. The following are the values of A,, B,, &c. for Bombay to first approxi- 
mations, to which point the analysis has at this time been completed :— 
8 K L M N oO 
(y—1) (y) (y-4e-4~) (y-2)  (y—-$e+45%) (y—20) 
A, —0'4488 —1'0522 +0°0168 +0'0713 —0'0380 +0'0777 
B, +0°6221 —04854 —0'2350 —o'0782 —o'O412 —6°5523 
A, +1°8245 —o'8071 —o'2669 +4°3095 +0'7291 —oroorr 
B, +0475 = +0°3340 9 —o'1679 = —0'2053 = 06429 = 071524. 
A, —0°0059 —0°0270 +o0'0172 —0°0475 +0'0132 +o'0l43 
B, —0'0079 +o'0113 +0'0024 —0'0664 +or0081 +0°0185 
A, -+0°0056 +0°0075 —0'0366 +o'1008 +0'0064 070000 
B, —0°0215 +o'0061 —0'0284 +o'ol12 00026 — 070042 
A, +0'0067 —o'0048 +0'0003 -+0'0003 —0'0029 +0°006r 
B, —0'0096 —o0°0066 —o'0108 —o'o102 +0'0123 —0°0034. 
A, +0'0045 —0'0051 +ororrr -+-oroorg —0°'0029 —0'0031 
B, +0'0006 —O°OOI7 -+-0°0070 —0'0234. +0°0093 —o°004.1 
A, —0°0005 —0°0026 —o'o108 +0'0049 -+o'o021 —o'0061 
B, —o'0041 —0°0005 + 0°0041 +0°0060 -+o'0050 0'0054. 
A, —0'0036 +0'0013 +0'0078 —0'00l3 -+-070048 —0'0036 
B, —o'oo1o —o*ooor +-0'0002 —O°0013 +o'0018 -+0'0029 
A, 8:2004 82017 82015 82054. $:2010 $:1970 
The series computed from these terms agree to a’ remarkable extent with 
the series from which they were deduced. 
38. The observations taken at Ngaloa, in the Fiji Islands, mentioned at 
§ 26, have not at present been completely reduced, the computations being 
still in the same state as at the date of the Meeting of the British Association, 
but will again be shortly taken up. 
39. Before closing this Report it may not perhaps be inappropriate to refer 
to a few among the innumerable benefits that may be anticipated from a 
better knowledge of the laws of the tides. Among the scientific results which 
are likely to be deduced from the foregoing system of analysis of tide-obser- 
vations, are an evaluation of the mass of the moon, definite information 
regarding the rigidity of the earth, an approximation to the depth of the sea 
from the observed velocities of tide-waves, and the retardation of the earth’s 
rotation due to tidal friction. Physical geography will probably gain some 
knowledge as to the amount of water-surface in the hitherto unexplored 
districts of the Arctic and Antarctic regions, and more reliable information 
with respect to the origin, direction, and progress of tide-currents over the 
surface of the oceans. The effect of atmospheric pressure will be estimated, 
and also an approximation due to the effect of wind on the height of the tide 
from the simultaneously observed direction and force of the wind at different 
ports. 
And the practical benefits to be derived from an accurate knowledge 
of the height of the tide at any time are certainly very great. Among 
them may be mentioned the navigation of large ships over shoals and bars, 
the docking, undocking, launching, and hauling up of vessels, and the 
floating off of stranded ships, and the working of small craft,—all operations 
in preparing for which a more or less exact foreknowledge of the tidal move-. 
ments is required. The preservation of property, and the protection of un- 
finished works from the overflowing of rivers at very high tides, and engi- 
oe works carried on between high and low water, may be powerfully 
aided. 
