44 REPORT—1885. 
IV. A Comparison oF THE Harmonic TREATMENT OF TIDAL OBSERVATIONS 
WITH THE OLDER MeETHops. 
§ 1. On the Method of Computing Tide-tables. 
There is nothing in the harmonic reduction of tidal observations 
which necessitates recourse to mechanical prediction of the tides. It 
may happen that it is desirable to produce a tide-table by arithmetical 
processes, and that the computers prefer to use the older methods of 
corrections, or it may be desired to obtain the tidal constants in the har- 
monic notation from older observations. For either of these purposes it 
is necessary to show how the harmonically expressed results may be 
converted into the older form, so that the constants for the fortnightly 
inequality in time and height, and the corrections for parallax and 
declination, may be obtained from those of the harmonic analysis, and 
conversely. 
In the following sections I propose, therefore, first to reduce the har- 
monic presentment of the resultant tide into the synthetic form, where 
we have a single harmonic term depending on the local mean solar time 
of moon’s transit, and on corrections depending on the R.A., declination, 
and parallax of the perturbing bodies. Subsequently it will be shown 
how a synthesis may be carried out more simply by retaining the mean 
longitudes and elements of the orbits. 
§ 2. Notation for Mean Heights and Retardations derived from the Harmonic 
Method. 
The notation of the Report of 1883 is adopted ; and I shall carry the 
approximation to about the same degree as has been adopted by the older 
writers. Closer approximation may, of course, be easily obtained. 
In the Report of 1883 the mean height of a tide is denoted by H, 
and the retardation or lag by x. In the present note it will be necessary 
to refer to several of the H’s and «’s at the same time, and therefore it 
is expedient to introduce the following notation :— 
Schedule III. 
Initial of | Mean height} Retardation | Initial of | Mean height | Retardation 
tide (H) (Kk) | tide (H) (k) 
M, M Qu Li L Od 
6 iS ar T T Or 
Lunar K, Je 2« R R 26 
Solar K, NGL 2 O M’ pe! 
Ke Ky 2 | P S! fel 
N N 2y K, K, Ky 
In this schedule we assume T and R (of speeds 2y—3n and 2y—n) to 
have the same lag as S,; and we use v in a new sense, the old v, the 
1 T use height to denote semi-range. All references to this Report will simply 
be by the date 1883. ‘ 
