376 Prof. G. H. Darwin. On an Apparatus for [Dec. 15, 



&A.J = + 0-0304 A 0-0171 ~B m , 



Bi = 0-0171 A OT 0*0304 Bwt, 



C = Ai + SAi, D = B! + ^BX. 



C 0-047 D = 0-992 fS" cos , 



D +0-047 C = 0-992 iH sin ^ 



Whence f being known from Baird's manual (being a function of 

 the longitude of moon's node), H and are determinable. We have 

 also 



In the set of computation forms which I have prepared for use on 

 the present plan, it is shown what days are to be erased for each of 

 the three analyses, and how they are to be entered in schedules, 

 summed, and analysed. 



9. On abridgment in the computations. 



It seemed probable that one decimal of a foot would suffice to 

 express the hourly tide heights. In order to test this, I have taken 

 several individual days of observation at Port Blair, and have found, 

 by harmonic analysis, the time and amplitude of the diurnal and 

 semi-diurnal H.W., first, when the hourly heights are expressed to 

 two decimal places of a foot, and secondly, when they are only 

 entered to the nearest tenth of a foot. I find that the times of H.W. 

 agree within less than a minute of time, and that the amplitudes 

 agree within a fraction of an inch. If this much be true of indi- 

 vidual days, the difference of results arising from two or one place of 

 decimals will clearly entirely disappear when a series of days is con- 

 sidered. Hence, by taking as unit the tenth of a foot, or the inch, or 

 even two inches at places with large tides, we may always express all, 

 or nearly all, the heights on which we are to operate by two signifi- 

 cant figures. The adoption of this rule not only saves the writing of 

 a large number of figures, but also enormously diminishes the labour 

 of the additions which have to be made. 



It also seemed probable that substantial accuracy might be attained 

 from the harmonic analysis of only 12 hourly values instead of 24. 

 In order to test this I took the tidal reductions for Port Blair, 

 Andaman Islands (kindly lent me by the Survey of India), and have 

 compared the results which would have been derived from 12 values 

 with those actually obtained from 24 values by the computers of the 

 Indian Survey. The following tables give the results : 





