1892.] facilitating the Reduction of Tidal Observations, 367 



_ 



3) ' 



If there be several months available it is recommended that each 

 30 days be treated quite independently, so that from each gronp of 

 days we shall get H', K' and H s , K S . Then the mean value of 

 H' cos K is to be taken as the final value of that function, and T sin K 

 is to be treated similarly ; finally H', K are to be found. The several 

 values of H s , K S may be treated in the same way. Of course we 

 assume throughout that K P = *', H p = %H', K" = K S , H" = -rr-H" 5 , as- 

 sumptions which are usually nearly correct. 



The mean value of ^o must be taken as giving AO, but at places 

 with a considerable annual tide it is impossible to obtain a good 

 value of mean water mark from a short series of observations. 



6. On the evaluation of the several tides by grouping of mean 

 solar days. 



Let ^(7 x) denote the speed in degrees per m.s. hour of any one 

 tide, n being equal to 1, 2, 3, 4, 5, or 6. Then 15/(7 x) ma Y be 

 called one " special hour." Since 15/(7 17) is one m.s. hour, the 

 ratio of the m.s. to the special hour is (7 x)/(7~ ^)- 



Let one m.s. hour be equal to 1 ft special hour, then 



ry x 



8 = 1 -- . special hours. 

 7-f' 



Let it be required to express the 12 h of any m.s. day of a series of 

 days by reference to special time. It is clear that 12 h m.s. time will 

 bje specified by one of the 24 special hours, with something less than 

 half a special hour added or subtracted. 



Having fixed the 12 h of m.s. time of a particular m.s. day in 

 the special time scale, let us treat that m.s. day as a whole, and 

 consider the incidence of the other 23 m.s. hours in special time. It 

 is clear that in m.s. time we work backwards and forwards from 12 h 

 by subtracting or adding unity, and that in special time we subtract 

 or add 1 /3. 



If 12 h m.s. time be aj h +a, where a lies between | special time, 

 the following is a schedule of equivalence : 



