1891.] On Tidal Prediction. 131 



Government renders the prediction comparatively cheap, yet the 

 instrument can hardly be deemed available for the whole world, and 

 the cost of publication is so considerable that the instrument cannot, 

 or at least will not, be used for many ports at remote places. It is 

 not impossible, too, that national pride may deter the naval authorities 

 of other nations from sending to London for their predictions, 

 although the instrument may, I believe, be used on the payment of 

 certain fees. 



The object, then, of the present paper is to show how a general 

 tide table, applicable for all time, may be given in such a form that 

 any one with an elementary knowledge of the Nautical Almanac 

 may, in a few minutes, compute two or three tides for the days on 

 which they are required. The tables are also such that a special tide- 

 table for any year may be computed with comparatively little trouble. 



Any tide-table necessarily depends on the tidal constants of the 

 particular port for which it is designed, and it is supposed in the 

 paper that the constants are given in the harmonic system, and are 

 derived from the reduction of tidal observations. Where the obser- 

 vation has been by tide-gauge, the process of reduction is that 

 explained in the Report to the British Association for 1883, but where 

 the observations are only taken at high and low water, a different 

 process becomes necessary. I have given in a previous paper a scheme 

 of reduction in these cases.* 



At ports not of first-rate commercial importance observation has 

 rarely been by tide-gauge, and thus it is exactly at those ports, where 

 the method of this paper may prove most useful, that we are deprived 

 of the ordinary method of harmonic analysis. On this account I 

 regard the previous paper as preliminary to the present one, although 

 the two are logically independent of one another. 



In the harmonic method the complete expression for the height of 

 water at any time consists of a number of terms, each of which 

 involves some or all of the mean longitudes of moon, sun, lunar and 

 solar perigees ; there are also certain corrections, depending on the 

 longitude of the moon's node. The variability of the height of water 

 depends principally on the mean longitudes of the moon and the sun 

 and to a subordinate degree on the longitude of lunar perigee and 

 node, for the solar perigee is sensibly fixed. There are, therefore, 

 two principal variables, and two subordinate ones. This statement 

 suggests the construction of a table of double entry for the varia- 

 bility of tide due to the principal variables, and of correctional 

 tables for the subordinate ones ; and this is the plan developed in the 

 paper. 



The mean longitudes of the moon and sun are not, however, con- 

 venient as variables, and accordingly the principal variables in the 

 * ' Hoy. Soc. Proc.,' 1890, vol. 48, p. 278. 



