Computation of Tides: Results of Theory and Observation Author(s): James Pearson Source: Proceedings of the Royal Irish Academy. Science, Vol. 3 (1883), pp. 656-660 Published by: Royal Irish Academy Stable URL: http://www.jstor.org/stable/20490131 . Accessed: 15/06/2014 13:49 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. . Royal Irish Academy is collaborating with JSTOR to digitize, preserve and extend access to Proceedings of the Royal Irish Academy. Science. http://www.jstor.org This content downloaded from 91.229.229.162 on Sun, 15 Jun 2014 13:49:40 PM All use subject to JSTOR Terms and Conditions
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Computation of Tides: Results of Theory and ObservationAuthor(s): James PearsonSource: Proceedings of the Royal Irish Academy. Science, Vol. 3 (1883), pp. 656-660Published by: Royal Irish AcademyStable URL: http://www.jstor.org/stable/20490131 .
Accessed: 15/06/2014 13:49
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LXXXVIII.-CCOMPUTATION OF TIDES-lRESULTS OF THEORY AND OB BERVATION. By JAMES PEARSON, M. A., Ex-Scholar (1 5th Wrangler) of Trinity College, Cambridge; Vicar of Fleetwood. (With Plate XIX.)
[Read, November 13, 1882.]
THE subject of Tides, upon which, from time to time, I have had the honour of addressing the Royal Irish Academy, is one of which the importance can hardly be overrated, whether we regard it in its con nexion with physical science or in its reference to practical naviga tion. A ship, on arriving at her port of destination, requires a safe access and convenient place of discharge, and these cannot be secured unless it is ascertained that a sufficient depth of water will be found to keep her afloat, and that a suitable time has been fixed upon for her entrance into the tidal harbour. Hence the exigencies of the case demand strict attention be paid to the amount of rise and fall of tide. A rough guess is not sufficient; an error of a few inches may cause the vessel to take the ground, and so to be left high and dry twice in twenty-four hours; and this for several days, in fact until the return of spring tides supplies water enough for her draught. Now this has a double inconvenience and loss. There is the expense of delay in her discharge, which is often very considerable-wages incurred without
work, and time idly squandered. If an attempt is made to lighten her by removing some of her cargo, it may be unsuccessful, and involves expenditure. More than this, the grounding of a ship of magnitude and in full load is most injurious. A severe strain takes place from the effects of which she can hardly ever be recovered; and if the ground be very hard and uneven, she may "Ibreak her back." Now these are not exaggerated dangers; and therefore whatever can be done to prevent their occurrence is a real boon to mercantile interests.
Impressed with these considerations, and having all the theoretical information on the subject which a knowledge of mathematics could supply, combined with an ardent love of what I may call an " unfre quented study," with the singular advantage of having my home within two hundred yards of a self-registering tide-guage, I have for the last twelve years practically applied myself, not only to the main problem, but also to the discrepancies involved in consequence of atmospheric disturbances, and evidence is now forthcoming to show that the success has been very remarkable. Self-praise is no recommendation, but those who have used the Admiralty Tide Tables for Liverpool during the last five years, have been prompt to testify to the improvement
which has taken place in their predictions of the height of tides. The calculations now are based on a modification of Bernouilli's, or the Equilibrium Theory; and the figures emplovedl were, in the first in stance, taken from Sir John 'W. Lubbock's tElementary T'reatise on
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the Tides." But "the principle of the method is one which never occurred to either of these philosophers, nor, if known at all, has it been published by anyone else. The principle involved is this: that the configuration of land and water on the surface of the globe brings it to pass that the direction of the moon's motion in respect to the equator makes a very great difference in the magitude of the tide wave which reaches our shores. For when the moon advances from south to north declination, crossing the equator, as she sometimes does, at an angle of 28 degrees, it is seen that her line of motion approxi
mately coincides with the general trend of the Atlantic Ocean, at the time when the earth's rotation brings that part of the globe directly beneath her, and this causes a further development of the tide-wave in the direction of Europe and North America; whereas, when the
moon declines from north declination to south, her course is diagonal to the former one, crossing the Atlantic, roughly speaking, in the direction of its breadth, whilst in the other case she crossed in the direction of its length. The like phenomena take place in connexion
with the obverse action of the moon on the opposite side of the globe, when that is the agency considered. The same remarks also apply in regard to the action of the sun, only this action is much more gradual and constant. Following out the principles thus briefly enumerated, a patient attention to the actual phenomena for twelve years has enabled me to draw up tables of computation which include every possible cause which can effect or interfere with the working of the tides.
Other principles of computation, however, have found favour with the Tidal Committee of the British Association, for the details of which the Annual Reports must be consulted. In the " Harmonic Analysis of the Tides," as it is called, the various changes of level to which the sea is subject) moment by moment, in consequence of the tide-generat ing forces, are ascertained by the enumeration of a series of Harmonic
Functions, each of which involves the time for which the computation is made, certain quantities depending on the angular velocity of the earth's rotation, the rates of relative orbital motion of the moon and sun, and certain constants. The relative merits of these rival theories (for such they are, though to a certain extent based on common funda
mental physical laws) can only be tested by comparison with observa tion, and for this purpose no place is more eligible than Liverpool,
where the equinoctial tides sometimes range as far as thirty-one feet from low-water. I am not aware, however, that this has been done.
Meantime, I desire to send to the Academy a sort of challenge-list of comparisons, taken for a semi-lunation in the month of June, 1882. The atmospheric conditions during this period were exceedingly con stant, and so. they very slightly affect the results. I am now engaged in forming a Table, the arguments of which are the direction and force of the wind on the one hand, and the height of the barometer on the other. By the aid of this, predictions may be made with much accuiracy in unsettled weather.
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_ _ _ _ _ _____ I _____~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
f3ut, in order to submit the newly-devised method to a still more severe and crucial test, it is necessary to examine what may be called correlative tides, i.e. tides having nearly the same constituents: for as like causes produce like effects in nature, such tides should show the same agreement between theory and observation. This plan becomes
more simple, because any one tide in any year has only one tide corre sponding to it in any other year; and if there be a discordance, it must be due to a difference in atmospheric conditions, and will indicate the change of height of tide arising from this cause.
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The above are favourable specimens: all others are not equally so. We shall next examine the atmospheric conditions which seem to account for the variation. Thus, if we take the Lunar and Solar Tides of August, which are incident to the moon's transit between 1 lh. and noon in the same years, with the atmospheric conditions
I Years. Moon's Moon's Dec Calcula- Obser- Baro Yer. Trans. Par. .Desc. tion. vation. meter. Wid .
So long as the-attospheric conditions are not very diverse, it is found that the agreement between theory and observation is very nearly perfect; the changes in the moon's parallax and declination, each producing their own separate effects with undeviating regularity, but when the atmospheric conditions change the effects become apparent. Thus, for the March Tides, lunar and anti-solar, transits between 4h. and 5h., P.M.
Moon's Moon's Moon's Calcula- Obser- Baro- Wind &cc Years. Trans. Par. S desc. tion. vation. meter.
The last tide would have had its height augmented by the direction and force of the wind, but this was counteracted by the high barome tric pressure.
In conclusion, enough has been said to show the progress made in accurate calculatiofi, and the data upon which the effects of atmos pheric conditions may be estimated. A similar method may be applied in the case of any other ports to which attention may be directed. For instance, in the case of Kurrachee, it is found that the diurnal inequa lity is very visible, when the moon or anti-moon is south of the equator at the instant of the transit, which occurs twelve hours previously. The configuration of land and water affects the course of the tides as certainly in the Indian as in the Atlantic Ocean; everywhere it pro duces irregularities which cannot be ignored, when special tide-tables have to be calculated.
Plate XIX. represents the curves formed by the tides, as observed by W. Parkes, E.C., at Kurrachee, and referred to in the Report of the British Association for 1870. It shows, by means of the graphic pro cess at the foot of the diagram, the law of the " diurnal inequality," for that place. For an explanation of this process see these Proceed ings, antea, page 73. The law is this: when the moon is below the equator, the lunar tides (combined with the solar) are highest, and arrive at Kurrachee about twelve hours after the transit B. When the anti-moon is below the equator, the anti-lunar tides (combined
with the anti-solar) are highest. The diurnal and semi-diurnal curves are also shown.
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