40 The Rev. Samuel Haughton on the Solar and Lunar 



The apparent height of the tide at any moment is made up of several quanti- 

 ties, of which the principal are: — 



1. The Semi-diurnal Tide. 



2. The Diurnal Tide. 



3. Tides of long period, depending on the change of position of the Sun and 

 Moon, or the Semi-menstrual and Semi-annual Tides. 



4. Elevation or depression of the water, due to slow changes of barometric 

 pressure. 



5. Abrupt changes due to wind. 



It is possible, by the following method, to separate in the observed High 

 and Low Waters the part due to Diurnal Tide, and abrupt changes due to wind, 

 from the first, third, and fourth quantities just mentioned. 



Let hi, hi, As, h^, h^, be five successive High or Low Waters ; the parts of these 

 heights due to the first four causes can be represented by sines and cosines. 

 Let A cos ?z0 be the height due to any periodic cause, <p being an arc of fixed 

 magnitude, and n a quantity increasing with the time in such a way that it is 

 increased by unity in the interval between two High or Low Waters, i. e., in 

 about 12" 24". 



From this definition we have, 



hi = A cos (n — 2) (j), 

 h^ = A cos (n — 1) ((), 

 hs — A cos 7i(j), 

 hi = A cos (n-f 1) (f>, 

 h^ = A cos {ii+ 2) 0. 



Taking the fourth difierence, we have, after some transformations, 



Fourth Difference = h^ — Ah^ + 6/(3 — 47*4 + A5 — l&A cos n<p sin^|0. 



The right-hand member of this equation disappears for all the terms except 

 the Diurnal Tide, and the abrupt changes of level caused by wind, which can- 

 not be eliminated. In the Semidiurnal Tide the value of is nearly 360°, 

 and consequently sin*^0 is evanescent. For the tides of long period, such as 

 those under the third and fourth heads, it is a very small angle ; for example, 

 in the Semi-menstrual Tide ^ is about 12° 37'; and, therefore, 



