TIDAL OBSERVATIONS. 501 
(y—3.0+4 am) Series. (y—2c) Series. 
=== ==> nae LE Sp a a 
Calculated. Observed. Difference. Calculated. Observed. Difference. 
(1) (2) (1)—(2) (1) (2) (1)—(2) 
10°9849 10°9688 +o'o16r 98166 9°3427 —o'0261 
10°5382 105528 —o'0146 9°8354 9'8278 +0'0076 
10°0146 10°0059 +0°'0087 9°9348 9°9300 4+0°0048 
94882 94898 —o'o0o16 10'0573 100630 —0'0057 
91314 91350 — 070036 10°1567 10°1549 +o'o018 
g 1141 91095 +0°0046 10°2547 10°2565 —o'oo018 
9°3896 93920 — 070024 10°3529 10°3448 -+0°0081 
98195 98203 —0'0008 104185 10°4312 —0'0127 
10°3658 10°3630 +0'0028 10°4357 10°4260 +0°0097 
10°9264 10°9284 —0'0020 10°4499 10°4515 —o'0016 
112698 11'2707 —0*0009 10°4696 10°4.704. —o0'0008 
11'2642 11°2602 +0'0040 10°4270 10°4348 —o'0078 
10°9573 10°9627 —0°0054 10°3790 10°3569 +0'0221 
10°4766 10°4723 +0°9043 IO"41I4 10°4368 —0'0254 
9°9446 99460 —o'0014 10°4014 10°3937 +0°0077 
9°4472 9°4479 —0'0007 10°3101 10°2850 +0°0251 
91166 9°1163 +0°0003 10°2987 10°3500 —0'0513 
91059 91028 +0°0031 10°3189 10°2643 +0°0546 
9°3910 9°3987 —0'0077 10°2291 10°2642 —0'0351 
9°8357 98248 -+o'o109 10°1271 10°1163 +o0'0108 
10°3834 10°3934 —o'oI0o 10°0589 10'0606 —0*'0017 
10°9362 10°9320 +0'0042 9°9363 9°9238 +0°0125 
11°2746 I1‘2701 00045 9°8322 9'8620 —o0'0298 
112714 11°2833 —o'ollg 98190 9°7823 +0'0367 
20. In the averages for any one of the §, K, L, M, N, O tides explained above, 
the influence of each of the others is nearly eliminated because of the greatness 
of the number of periods (roughly 360 and 720) of each in the series of 
observed heights included in the summations. The choice of the approximate 
period 369° 3", as explained above (§ 16), makes «as little as possible of the 
mutual influence of the two largest tides, the lunar and solar semidiurnal 
tides, in the two averagings performed to determine these two tides. But 
the incommensurability of the periods renders it impossible to altogether 
escape, in the direct synthesis for any one tide, the influence of the others. 
Accordingly, the coefficients A,, B,, &c., shown above, are to be regarded as 
first approximations in the mathematical solution of the problem. The next 
step followed was to find corrections upon each summation for the influence 
of the tides determined by the other summations, these corrections, for a 
second approximation, being calculated on the supposition that the first 
approximate values of A,, B,, A,, &c., already found, are correct. An 
auxiliary Table (see § 15, above) for performing this process has been formed, 
and must be printed with rules for its use along with the other Tables; and 
therefore it is sufficient at present to state the results for Ramsgate 1864. 
The corrections thus formed are to be subtracted from the values of A,, A,, 
&e., to first approximation, and are as follows :— 
21. Table of Corrections of the 6 x 16 Coefficients A,, B,, &e. 
8 K L M N O 
(y—n) (y)  (y-8e-4@) (y-9) (y—-3e+3a) (y—20) 
A, —"0025 —"o002 —"0021 +:0087 Ors —"0032 
B, +0015 +0001 —"0050 —*0003 +-0032 +°0056 
A, —oo18 —'0313 +:0065 —*0009 +:0093 —"o188 
B, —"o104 +'0105 —'0338 +0033 +cor1or —"0008 
A, +*0009 +0087 —*0074. —"0025 —"ooor —*0063 
13% — "0004. —*0074. +0152 —"ools +'0044. -+"0032 
