52 KEPORT — 1886. 



and add 1. This rule depends on the fact that the moon's mean parallax 

 in radians is ^}q. 



For the purpose of applying the corrections c,R„, ^2^1.1) ^•I'-'mi C2^, 

 r.>y, it is most convenient to compute auxiliary tables for each degree of 

 declination of the moon and minute of her parallax, and then the actual 

 corrections are easily applied by interpolation. 



These tables serve for the port as long as the longitude of the moon's 

 node is nearly constant, or with rougher approximation for all time. 



The declinational and parallactic corrections to high water depend on 

 the moon's declination and parallax at a time anterior to high water by 

 ' the age.' Hence, in order to find these corrections we have to know the 

 time of high water in round numbers. Each high water follows a moon's 

 transit at the port approximately by the interval ■>'. The Greenwich 

 time of the moon's transit at the port is the G.M.T of moon's transit 

 at Greenwich, less 2 minutes for each hour of E. lougitude, less the E. 

 longitude in hours. Then, if we subtract from this ' the age ' and add the 

 interval i, we find the G.M.T's at which we want the moon's declination 

 and parallax. 



Thus, at Port Blair) m MT^f t>'c^ 

 the G.M.T. at which =^^f^^,°^^« -long. corr. for transit (0-2) 

 we want parx. and decl. ' 



— E. long, of port (6'^-2)-age of tide (32''-6) 



+ mean interval (9'^*6) 

 = G.M.T of ]) 's tr. at Gr.— 29''4. 



Thus at Greenwich, on Feb. 1st, 1885, the moon's lower, transit was 

 at 2'', and hence, corresponding to the lower transit at Port Blair of 

 Feb. 1, we require the moon's parallax and declination at 21'' Jan. 30, 

 G.M.T. The parallax at the nearest Greenwich noon or midnight is 

 sufficiently near the truth, and therefore we take the parallax at 0'' Jan. 31, 

 which is 60'-0, and the excess above the mean is 3'-0, and 1 + 3 sin 3° is 

 1-157, which is the factor p'. Actually, however, we read off the correc- 

 tion CyR^ and the other corrections ^2^m, ^zh hr straight from the 

 auxiliary tables. 



§ 7. On Tide-tables Computed hy the above Method. 



A great deal of arithmetical work was necessary in making trial of the 

 rules devised above and in various modifications of them, and I must 

 record my thanks to Mr. Allnutt, who has been indefatigable in working 

 out tide-tables for various ports, and in comparing them with official 

 tables. The whole of the results, to which I now refer, are due to him. 

 The following table exhibits the amount of agreement between a com- 

 puted table and one obtained by the tide-predicting instrument. It must 

 be borne in mind that the instrument is rigorous in principle, and makes 

 use of far more ample data than are supposed to be available in our 

 computations. The columns headed ' Indian tables ' are taken from the 

 official Indian tide-tables. The datum level, however, in those tables is 

 3-13 ft. below mean water mark, whereas ' Indian spring low-water 

 mark ' is 3-65 ft. below the mean. Thus, to convert the heights given in 

 the Indian tables to our datum 0-42 ft. or 5 ins. have been added to all 

 the heights in the official table. 



