HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 93 
henceforth treated, and to give the requisite information for the sub- 
sequent use of the tide-predicting instrument. 
The tide-gauge furnishes us with a continuous graphical record of the 
height of the water above some known datum mark for every instant of 
time. 
It is probable that at some future time the Harmonic Analyser of 
Professors James and Sir William Thomson! may be applied to the tide- 
curves. The instrument is nearly completed, and now lies in the Physical 
Laboratory of the University of Glasgow, but it has not yet been put into 
use. The treatment of the observations which we shall describe is the 
numerical process used at the office of the Indian Survey at Poona, under 
the immediate superintendence of Major A. W. Baird, R.E. The printed 
forms for computation were admirably drawn up by Mr. Edward Roberts, 
of the ‘ Nautical Almanac’ Office ; but they have now undergone certain 
small modifications in accordance with this Report. The work of compu- 
tation is to a great extent carried out by native Indian computers. The 
results of the harmonic analysis are afterwards sent to Mr. Roberts, who 
works out the instrumental tide-predictions for the several ports for the 
ensuing year. The use of that instrament requires great skill and care. 
The results of the tidal reductions have hitherto been presented in a 
somewhat chaotic form, and we believe that it is only due to Mr. 
Roberts’ knowledge of the manner in which the tidal results have been 
treated that they have been correctly used for prediction. It may be 
hoped that the use of the methods recommended in the present Report 
will remove some of the factitious difficulties in the use of the instru- 
ment. 
The first operation performed on the tidal record is the measurement 
in feet and decimals of the height of water above the datum at every 
mean solar hour. The period chosen for analysis is about one year, and 
the first measurement corresponds to noon. It has been found im- 
practicable to make the initial noon belong to the same day at the several 
ports. It would seem, at first sight, preferable to take the measurements 
at every mean lunar hour; but the whole of the actual process in use is 
based on measurements taken at the mean solar hours, and a change to 
lunar time would involve a great deal of fresh labour and expense. 
If T be the period of any one of the diurnal tides, or the double period 
of any one of the semi-diurnal tides, it approximates more or less nearly 
to 24 m. s. hours, and if we divide it into 24 equal parts, we may speak 
of each as a T-hour. We shall for brevity refer to mean solar time 
as S-time. 
Suppose, now, that we have two clocks, each marked with 360°, or 
24 hours, and that the hand of the first, or S-clock, goes round once in 24 
S-hours, and that of the second, or T-clock, goes round once in 24 7-hours, 
and suppose that the two clocks are started at 0° or 0® at noon of the 
initial day. For the sake of distinctness, let us imagine that a T-hour is 
longer than an S-hour, so that the T-clock goes slower than the S-clock. 
The measurements of the tide-curve give us the height of water exactly 
at each S-hour; and it is required from these data to determine the 
height of water at each T-hour. 
For this end we are, in fact, instructed to count T-time, but are only 
allowed to do so by reference to S-time, and, moreover, the time is 
always to be specified as an integral number of hours. 
" See Appendix, Thomson and Tait’s Nat. Phil. 2nd ed. 1883. 
