1892.] facilitating the Reduction of Tidal Observations. 365 



We thus get the following rule for the evaluation of A , S 5a , Si, S 2 , 

 S 4 , S 6 , K 2 , Ki, P from 6, 7, 8, 9, or 10 months of observation : 



Proceed as though the year were complete and find the Q's and $'& 

 for as many months as are available. Reduce the j^ 8 , ^ 3 by multiplica- 

 tion by 1/P< T > or 10-0504 cos (ft + 30T + 94 ). 



Analyse gi (r) , gii (T) , ^^ for annual inequality, and gi 2 /-P (T> , 2 (T V JD(T) 

 /or semi-annual inequality according to the rules for reduction of incom- 

 plete series just given. 



Complete the reduction as in 3. 



These rules for reduction do not include the case of 11 months, 

 nor the case where any month in the series is incomplete (e.g., if a 

 fortnight's observation were wanting in one of the months), because 

 these cases may be treated thus : the j^'s and |p's return to the same 

 value at the end of a year, and therefore the case of eleven months 

 is the same as that of a missing month at any other part of the year. 

 In both these cases we may interpolate the missing gt's and U's and 

 treat the year as complete. 



If three or more weeks of observation were missing they might fall 

 so as to spoil two months, and in this case we should have an in- 

 complete series. It is then to be recommended that the equations of 

 least squares be formed and the equations solved. So many similar 

 cases may arise that it does not seem worth while to solve the equations 

 until the case arises. 



5. Evaluation of AO, S 2 , S 4 , K 2 , K b P from a short period of 

 observation. 



If the available tidal observations only extend over a few months, 

 it is useless to attempt the independent evaluation of those tides 

 which we have hitherto found by means of annual and semi-annual in- 

 equalities in the monthly harmonic constants. We will suppose that 

 30 days of observations are available. Then when we neglect the 

 annual tide, and the solar (meteorological) tide Si, we have from (11) 

 or (17), which give the analysis of 30 days, 



-^E^ 



= H u ^ *, P = 1+0-0504 COS (Ac + 15). 



It is now necessary to assume that the P tide has the same 



