Page:EB1911 - Volume 26.djvu/980
§4. Tide-Tables and the Degree of Accuracy in Tidal Prediction.
[1]
—The connexion between the tides and the movements of the
moon and sun is so obvious that tidal predictions
were regularly made and published long before
mathematicians had devoted their attention to them; and these
predictions attained considerable success, although they were
Empirical
Tide-tables.
founded on empirical methods. During the 18th century, and
even in the earlier part of the 19th, the art of prediction was
regarded as a valuable family secret to be jealously guarded from
the public. The best example of this kind of tide-table was
afforded by Holden’s tables for Liverpool, founded on twenty
years of observation by a harbour-master named Hutchinson.[2]
Fig. 1.—Tide-curve for Bombay from the beginning of the civil year 1884 to the midnight ending Jan. 14, 1884,
or from 12h Dec. 31, 1883, to 12h Jan. 14, 1884, astronomical time.
About 1832 the researches of W. Whewell and of Sir John Lubbock (senior) pointed the way to improvement on the empirical tables prepared by secret methods, and since that time the preparation of tide-tables has become a branch of science.
A perfect tide-table would tell the height of the water at the place of observation at every moment of the day, but such a table would be cumbrous; it is therefore usual to predict only the times and heights of high-water and of low-water. The best kind of tide-table contains definite forecasts for each day of a definite year, and we may Prediction for each Day. describe it as a special table. Although the table is only made for one definite place, yet it is often possible to give fairly accurate predictions for neighbouring ports by the application of corrections both for time and height. Special tide-tables are published by all civilized countries for their most important harbours.
But there is another kind of table, which We may describe as a
general one, where the heights and times are given by reference
to the time at which the moon crosses the meridian.
Although such a table is only applicable to a definite
place, yet it holds good for all time. In this case it is
necessary to refer to the Nautical Almanac for the
Prediction by Reference to Time
of Moon’s Transit.
time of the moon’s transit, and a simple calculation
then gives the required result. In a general tide-table
the heights and times are tabulated according to the hour
of the clock at which the moon will cross the meridian at the
place of observation, distinguishing between the visible and
invisible transits. Certain simple corrections have also to be
applied. A considerable degree of elaboration has to be given
to the table, in order that it may give accurate results, and it
would occupy some half-dozen to a dozen pages of a book, its
extension varying according to the degree of accuracy aimed at.
It might occupy about five minutes to extract prediction from
the more elaborate form of such a table. There are many ports
of considerable commercial importance where, nevertheless, it
would hardly be worth while to incur the great and repeated
expenditure involved in the publication of special tables. But
this kind of elaborate general table has been used in few cases,[3]
and the information furnished to mariners usually consists
either of a full prediction for every day of a future year, or of
a meagre statement as to the average rise and interval, which
must generally be almost useless.
The success of tidal predictions varies much according to the place of observation. In stormy regions the errors are often considerable, and the utmost that can be expected of a tide-table is that it shall be correct with a steady barometer and in calm weather. But such conditions Meteorological Disturbance of Prediction. are practically non-existent, and therefore errors are inevitable.
Notwithstanding these perturbations, tide-tables are usually
of surprising accuracy even in northern latitudes; this may be seen
from the following table showing the results of comparison
between prediction and actuality at Portsmouth.
The importance of the errors in height depends, of
course, on the range of the tide; it is well, therefore, to
Amount of Error
at Portsmouth.
note that the average ranges of the tide at springs and neaps are
13 ft. 9 in. and 7 ft. 9 in. respectively.
Prediction at such a place as Portsmouth is difficult, on account
of the instability of the weather, but, on the other hand, the tides
in themselves are remarkably simple in character. Let
us now turn to such a port as Aden, where the weather
is very uniform, but the tides very complex on account
of the large diurnal inequality, which frequently
Amount of Error
at Aden.
obliterates one of two successive high-waters. The short series of
comprisons between actuality and prediction which we give below
may be taken as a fair example of what would hold good when a
long series is examined. The results refer to the intervals 10th of
March to the 9th of April and the 12th of November to the 12th of
December 1884. In these two periods there should have been 118
high waters, but the tide-gauge failed to register on one occasion,
- ↑ References may be given to two papers by G. H. Darwin on this subject, viz. “Tidal Prediction,” Phil. Trans., A. (1891) pp. 159–229; and “An apparatus for facilitating the reduction of tidal observations.” Proc. Roy. Soc. (1892), vol. lii. For a general account without mathematics see Darwin’s Tides, &c.; this section is founded on chs. xiii. and xiv. of that book. For mathematical methods see Maurice Lévy, Théorie des marées (Paris, 1898).
- ↑ Whewell, History of Inductive Sciences, ii. 248; Darwin’s Tides, &c., ch. iv.
- ↑ Darwin, “Tidal Prediction,” quoted above. This kind of table has been applied with some success at Cairns in North Queensland, where there is a large diurnal inequality.