1892.] facilitating the Reduction of Tidal Observations. 349 



Accordingly, the computing strips are made to suit a chosen type. 

 The standard length for one of the 24 divisions on the strips was 

 chosen as that of a " 2-em English quadrate"; 24 of these conie to 

 9 inches, which is the length of a strip. I found the English quadrate 

 a little too narrow, and accordingly between each line of quadrates 

 there is a " blind rule," of 42 to the inch. The depth of the guide sheet 

 is that of 74 quadrates and 74 rules, making 15J in. The computing 

 strips are in. broad, and 74 of them- occupy 14f in. The excess 

 of 15 above 14f , or T 7 F in., is necessary to permit the easy arrange- 

 ment of the strips. 



To guard against the risk of the computer accidentally using the 

 wrong sheet, the sheets are printed on coloured paper, the sequence of 

 colours being that of the luinbow. The sheets for days to 73 are all 

 red; those for days 74 to 74 -f 73> or 147, are all yellow; those for 

 days 148 to 148 + 73, or 221,. are green; those for days 222 to 

 222 + 73, or 295, are blue; and those for- days 296 to. 296 + 73, or 369, 

 are violet. 



Thus, when the observations for the first 74 days of the year are 

 written on the strips all the sheets will be red ; the strips will then 

 be cleaned, and the observations for the second 74 days written in, 

 when all the guide sheets will be yellow, and so on. 



I must now refer to another.- considerable abridgment of the process 

 of harmonic analysis. It is independent of the method of arrange- 

 ment just sketched. 



In the Indian computation forms the mean, solar hourly heights 

 have been found for the whole year, and the observations have been 

 rearranged for the evaluation of certain other tides governed by a 

 time scale which differs but little* from the mean solar scale. I now 

 propose to break the mean, solar heights into sets of 30 days, and to 

 analyse them, and next to harmonically analyse the 12 sets of har- 

 monic constituents for annual and semi-annual inequalities. By this 

 plan the harmonic constants for 11 different tides are obtained by 

 one set of additions. In* fact, we now get the annual, semi-annual, 

 and solar elliptic tides, which formerly demanded much troublesome 

 extra computation. A great saving is secured by this alone, and 

 the results are in close agreement with those derived from the old 

 method. 



The guide sheets marked S> and the computation forms are 

 arranged so that the observations, are broken up into the proper 

 groups of 30 days, and they show the computer how to make the sub- 

 sequent calculations. 



I have also devised an abridged method of evaluating the tides of 

 long period MSf, Mf, Mm. The method is less accurate than that 

 followed hitherto, but it appears to give fairly good results, and 

 reduces the work to very small dimensions. 



