1 :':.' On Tidal Prediction. [Jan. 29, 



tables are the time of moon's transit and the time of year ; whilst 

 the subordinate variables are the moon's parallax and the longitude of 

 her node. 



The tide-table, then, consists of the interval after moon's transit 

 and height of high and low water, together with nodal and parallactic 

 corrections, computed for every 20 of moon's transit, and for about 

 every ten days in the year. Each table serves for the two times of 

 year at which the sun's longitude differs by 180, and they may be 

 used without interpolation. The nodal correctional terms consist of 

 two times and of two heights, which are to be multiplied by the 

 cosine and sine of the longitude of the moon's node, to give the total 

 nodal corrections to the interval and height. The parallactic correc- 

 tional terms consist of a time and a height, which are to be multi- 

 plied by the excess above, or defect below 57' of the moon's parallax 

 at moon's transit to give the total parallactic corrections to the inter- 

 val and height. 



I had hoped that less elaborate tables might have sufficed, but it 

 appeared that, at a station with very large diurnal inequality, the 

 changes during the lunation, and with the time of year, in the interval 

 and height are so abrupt and so great, that short tables would give 

 very inaccurate results, unless used with elaborate interpolations. It 

 is out of the question to suppose that a ship's captain would or could 

 carry out these interpolations, and it is therefore proposed to throw 

 the whole of that work on to the computer of the table. 



Such a paper as this can only be deemed complete when an example 

 has been worked out to test the accuracy of the tidal prediction, 

 and when rules for the arithmetical processes have been drawn up, 

 forming a complete code of instructions to the computer. 



The port of Aden was chosen for the example, because its tides 

 are more complex and apparently irregular than those of any other 

 place which, as far as I know, has been thoroughly treated. 



The arithmetic of the example was long, and was re-arranged many 

 times. An ordinary computer is said to work best when he is igno- 

 rant of the meaning of his work, but in this kind of tentative work 

 a satisfactory arrangement cannot be attained without a full compre- 

 hension of the reason of the method. I was therefore fortunate ii 

 securing the enthusiastic assistance of Mr. J. W. F. Allnutt, and 

 owe him my warm thanks for the laborious computations he has 

 carried out. After computing fully half the original table, he made a 

 comparison for the whole of 1889 of our predictions with those of 

 the Indian Government. Without going into the details of this com- 

 parison, it may be mentioned that the probable error of the discrepancy 

 between the two tables was 9 in time, and 1'2 inches in the height 

 of high water ; that there were reasons to expect some systematic 

 difference between the two calculations, and that all the considerable 



