TIDAL OBSERVATIONS. 5038 
calculated by the average of several years. There is no tide corresponding 
strictly to them. 
A,, B, are, as they ought to be, very good approximations to zero in all 
the columns except M. Their values in this column constitute, probably, a 
genuine expression of the ter-diurnal lunar tide {not included in the pre- 
ceding general schedule (§ 2) but referred to in § 3], investigated by 
Laplace as depending on the fourth power of the moon’s parallax. 
A,, B, express shallow-water tides* derived from the lunar semidiurnal 
tide, according to precisely the same dynamical principle as that by which 
Helmholtz has explained the over-tones generated in very loud sounds, even 
when the source of the sound is a simple harmonic motion. There ought to 
be no sensible tide expressed by A, and B, in column L, and the comparative 
largeness of these numbers is probably an accident, owing either to errors of 
observation or the imperfection of the system of combination adopted, or a 
chance concurrence of disturbance due to wind &e. 
A,, B, in almost every column approximate remarkably well to zero; and 
even their greatest values (those of column §$) express merely a deviation 
of =, of a foot (or 0-3 of an inch) on each side of the mean level. 
A,, B, may be considered as insensible for every column except M, for 
which they express, as they ought to do, an undoubtedly genuine shallow 
water tide, being the second harmonic (as it were overtone) of the lunar 
semidiurnal tide. 
A,, B, are very good approximations to zero in all the columns. 
A,, B, in column M express probably.a genuine, though very small, 
shallow-water tide, the third harmonic of the lunar semidiurnal tide. 
There is a very good approximation to zero in all of the other columns. 
23. It is interesting, with reference to the mode of reduction which 
has been adopted, to remark to how nearly zero the comparatively large 
values of A., B, in column O, and A,, B, in column L of the first approxima- 
tion are reduced by the corrections found in the second approximation, 
explained above. Selecting from the preceding Table the coefficients which 
are each probably a genuine tide, and applying the proper correction 
(Everett, Roy. Soc. Edin. Trans. 1860) to take account of the circumstance 
that the mean height for each hour has been virtually taken for the height 
at the middle of the hour, we have the following, according to notation of § 2. 
Ss) K L M N O 
(y—n) (y) (y-ke-3e) (y-0) (y-$e+3a) (y—2c) 
R, 0'0373 0°2070 BE che O'OI45 bd 0°3008 
€, 313° 28"9 )©=— 186° 362 x 337° 589 eee 167° 51"0 
R, 1°8772 0°4279 0°3856 6°3078 1°1126 
€, 32° 42"2 182° 14"g9 127° 53"7 133° 48'4 «317° 246 
pee beoe Brafeya 0°0448 Jeysrs ofe\ ako 
€, aSor sores are 104° 57'°4 A600 : 
R, 070315 fees o°1078 0°5771 
&4 4 11"4 vane 239° 24"7 189° 1"'9 
R, 0'0268 door ne O'1771 
€, Da ae Dope goles 225° 8'°3 
R, eOee Bice Aetoc 9"0599 
€, Sich sia ae wists 305° 513 
* Tt is this term that makes the whole resultant tide rise faster than it falls, as is 
_ generally observed in estuaries, and other localities separated from the oceans by con- 
siderable spaces of shallow water. 
