53 The Rev. S. Haughton on the Solar and Lninar 



care ; aud I believe that, with good observers, the error in time 

 would be less thau oue minute. To the observers themselves, 

 who were all selected from the Coast-guards at each station, too 

 much praise can scarcely be given for the intelligence and patient 

 industry with which they succeeded in carrying out the rules for 

 observation in which they were carefully instructed ; and I believe 

 it is not too much to assert, that, so far as the observers were 

 concerned, it would be impossible to have an extensive series of 

 tidal observations made with greater care and accuracy. 



Section II. Method of discussing the Daily Observations. 



The daily observations consisted, as already mentioned, of 

 observations of all the apparent high and low waters occurring 

 each day. These observations of height were arranged in order 

 of occurrence, and the diurnal tide in height at high and low 

 water calculated from them, in the following way. 



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

 several quantities, of which the principal are, — 



1. The semidiurnal tide. 



2. The diurnal tide. 



3. Tides of long period depending on the change of position 



of the sun and moon, or the semimenstrual 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 ob- 

 served high and low waters, the part due to diurnal tide and 

 abrupt changes due to wind, from the 1st, 3rd, and 4th quan- 

 tities just mentioned. 



Let /ip ho, Jiq, 7*4, h^ be five successive high or low waters ; the 

 parts of these heights due to the first four causes can be repre- 

 sented by sines and cosines. Let A cos n<^ be the height due 

 to any periodic cause, ^ being an arc of fixed magnitude, and u 

 a quantity increasing with the time in such a way that it is in- 

 creased by unity in the interval between two high or low waters, 

 t. e. in about \2^ 24«'. 



From this definition we have — 



Aj = Acos [71— 2) (f) 

 ^2=Acos (?i — 1)^ 

 7/3= A cos n(f) 

 ^4= A cos {n+l)(j) 

 7«5 = Acos (n + 3)0. 



