

1892.] facilitating the Reduction of Tidal Observations. 387 



Sourly sums and harmonic analysis. 



Complete the summations in the forms for hourly sums, and copy 

 into the forms for harmonic analysis. In this copying it will gene- 

 rally suffice if the last figure in the hourly sums be omitted ; for 

 example, if the observations are entered to the nearest tenth of a foot 

 the hourly sums will be given in the same unit, and it will suffice if 

 the hourly sums analysed be written to the nearest foot. 



There are 12 analyses (one for each month of 30 days) for the 

 hourly sums in S, and one analysis for each of the other 10 arrange- 

 ments. All the forms are provided with spaces for 24 hourly sums, but 

 in the eight series N", L, *>, O, Q, J, fi, 2SM, where only 12 values will 

 commonly be used, the entries will only be made on the alternate 

 rows of O h , 2 h , . . . ., 22 h . In these cases the divisor 12, which occurs 

 in the penultimate stage of finding the A's and B's, must be replaced 

 by 6. 



The large divisors (viz., 369 for M, ^ 2SM, MS ; 369 for ; 358 

 for N", L, J, Q ; and 350 for v) represent the number of days under 

 reduction, and must be altered appropriately (see table, 7) if there 

 be long gaps in the observations, or if the year be incomplete, or if 

 the series be a short one. 



If some one of the monthly analyses of S is deficient the missing 

 gl's and g's are to be made good by interpolation.' 



It is then necessary to analyse the monthly values of the j^'s and 

 's derived from the 12 analyses of S. We thus obtain A , A : , B b 

 A 2 , B 2 , Co, c , d, D b c b d 1? Bo, e , E 15 F 2 , e 1} f b B 2 , F 2 , e z , f 2) . The rules 

 for these analyses when the year is incomplete are given in 4, and 

 the computation forms only apply to the case of the complete year. 



Astronomical data and final reduction. 



Determine from the ' Nautical Almanac ' and Major Baird's 

 ' Manual of Tidal Observations '* the astronomical data at O h local 

 M.T. on day 0, and proceed according to the form to find tne initial 

 arguments and factors for reduction. The astronomical data are then 

 to be used in the forms for final reduction. 



We have generally B = Rsin A = Rcos'; the forms are 

 arranged so that colog A is to be added to log B to find log tan , and 

 thence . If lies between -45 and 45 or between 135 and 225, 

 log sec is added to log A to find R ; if " lies between 45 and 135 

 or between 225 and 315, log cosec is added to log B to find R. 



Violet; between 4 h and 5 h ; shorts follow 2, 5, . . . . , 14; 18, 21, . . . . , 33 ; 37, 

 40,...., 52; 56, 59, ....,71. 



The last strip used for a year is 61. 



* Taj lor and Francis, London, 1886, price 7*. 6d. 



