r 



ON THE HAEMONIC ANALYSIS OF TIDAL OBSERVATIONS. 51 



In this way we find the corrections to the time of high water from and 



K, + P ; and since n=y-(T, and 5-^^= O'^'OSS, and !i'=l-^--^- for O, 



4<Trn n y — a 



and 1+ for K,, we Lave 



y — (7 



ato=-0'^-988 (l-^^\^' sin [l^t--Co-m°xn-\, 

 \ y—<yJ H 



at'=-0h-988 (\ + ^L\ ^ sin [15t-;' + l° x«J, . (25) 

 V y — tJ H 



where H is the height of the semidiurnal high water. 



With sufficient a^jproximation we may write these corrections : 



cto=-Px ^ sin [14°t-Co-25i°x«], 



?t'=-Px 5^sin [15°t-;' + l°XJi] .... (26) 



The computations are easily carried out, although the arithmetic is 

 necessarily tedious. Since two places of decimals are generally sufficient 

 for Ro and R', the multiplications by the sines and cosines are very easily 

 made with a Traverse Table. 



The successive high and low waters follow one another on the average 

 at 6h 12'" ; now, 14° x 6-2=87°, and 15° x 6-2=93°. Hence, if we compute 

 14!°t — Co — 25^° X ft for the first tide on any day, the remaining values are 

 found with sufficient approximation by adding once, twice, thrice 87° ; 

 and similarly, in the case of 15°t— <;' + l xn we add once, twice, thrice 

 93°. 



§ 6. Certain Details in the Computation of the Tide-table. 



It will be well to give some explanatory details concerning the manner 

 of carrying out the computations. 



The angle A is given by 16°-51 + 3°-44 cos Q, — 0°-19 cos 2 Q, where 

 ^ is the longitude of the moon's node. It is clear that A varies so slowly 

 that it may be regarded as constant for many months, and the same is 

 true of the factors f, f", f, f^, and the small angles v, I, v', 1v" . 

 Approximate formulae for these quantities in terms of Q, were given in 

 the Report of 1885, and are used in the article in the ' Manual.' 



To find the cube of the ratio of the sun's parallax to his mean parallax, 

 the following rule is given : Subtract the mean parallax from the parallax, 

 multiply the difference by 19|, read as degrees instead of seconds, look 

 out the sine, and add 1. This rule is founded on the fact that a mean 

 parallax 8"-85 multiplied by 19J gives 3 x 57", and 57° is the unit angle 

 or radian, whilst the sine of a small angle is equal to the angle in radians. 

 Similarly, the cube of the ratio of the moon's parallax to her mean 

 parallax is 



1 + 3 sin [60(parx — mean parx)]. 



That is to say, for the moon : Subtract the mean parallax from the paral- 

 lax, read as degi-ees instead of minutes, look out the sine, multiply by 3, 



e2 



