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Zetetic Astronomy, by 'Parallax' (pseud. Samuel Birley Rowbotham), [1881], at sacred-texts.com
The distance across St. George's Channel, between Holyhead and Kingstown Harbour, near Dublin, is at least 60 statute miles. It is not an uncommon thing for passengers to notice, when in, and for a considerable distance beyond the centre of the Channel, the Light on Holyhead Pier, and the Poolbeg Light in Dublin Bay, as shown in fig. 23. The Lighthouse on Holyhead
[paragraph continues] Pier shows a red light at an elevation of 44 feet above high water; and the Poolbeg Lighthouse exhibits two bright lights at an altitude of 68 feet; so that a vessel in the middle of the Channel would be 30 miles from each light; and allowing the observer to be on deck, and 24 feet above the water, the horizon on a globe would be 6 miles away. Deducting 6 miles from 30, the distance from the horizon to Holyhead, on the one hand, and to Dublin Bay on the other, would be 24 miles. The square of 24, multiplied by 8 inches, shows a declination of 384 feet. The altitude of the lights in Poolbeg Lighthouse is 68 feet; and of the red light on Holyhead Pier, 44 feet. Hence, if the earth were a globe, the former would always be
[paragraph continues] 316 feet and the latter 340 feet below the horizon, as seen in the following diagram, fig. 24. The line of sight H, S, would be a
tangent touching the horizon at H, and passing more than 300 feet over the top of each lighthouse.
Many instances could be given of lights being visible at sea for distances which would be utterly impossible upon a globular surface of 25,000 miles in circumference. The following are examples:--
"The coal fire (which was once used) on the Spurn Point Lighthouse, at the mouth of the Humber, which was constructed on a good principle for burning, has been seen 30 miles off." 1
Allowing 16 feet for the altitude of the observer (which is more than is considered necessary, 2 10 feet being the standard; but 6 feet may be added for the height of the eye above the deck), 5 miles must be taken from the 30 miles, as the distance of the horizon. The square of 5 miles, multiplied by 8 inches, gives 416 feet; deducting the altitude of the light, 93 feet, we have 323 feet as the amount this light should be below the horizon.
The above calculation is made on the supposition that statute miles are intended, but it is very probable that nautical measure is understood; and if so, the light would be depressed fully 600 feet.
The Egerö Light, on west point of Island, south coast of Norway, is fitted up with the first order of the dioptric lights, is visible 28 statute miles, and the altitude above high water is 154 feet. On making the proper calculation it will be found that this light ought to be sunk below the horizon 230 feet.
The Dunkerque Light, on the south coast of France, is 194 feet high, and is visible 28 statute miles. The ordinary calculation shows that it ought to be 190 feet below the horizon.
The Cordonan Light, on the River Gironde, west coast of France, is visible 31 statute miles, and its altitude is 207 feet, which would give its depression below the horizon as nearly 280 feet.
The Light at Madras, on the Esplanade, is 132 feet high, and is visible 28 statute miles, at which distance it ought to be beneath the horizon more than 250 feet.
The Port Nicholson Light, in New Zealand (erected in 1859), is visible 35 statute miles, the altitude being 420 feet above high water. If the water is convex it ought to be 220 feet below the horizon.
The Light on Cape Bonavista, Newfoundland, is 150 feet above high water, and is visible 35 statute miles. These figures will give, on calculating for the earth's rotundity, 491 feet as the distance it should be sunk below the sea horizon.
The above are but a few cases selected from the work referred to in the note on page 29. Many others could be given equally important, as showing the discrepancies
between the theory of the earth's rotundity and the practical experience of nautical men.
The only modification which can be made in the above calculations is the allowance for refraction, which is generally considered by surveyors to amount to one-twelfth the altitude. of the object observed. If we make this allowance, it will reduce the various quotients so little that the whole will be substantially the same. Take the last case as an instance. The altitude of the light on Cape Bonavista, Newfoundland, is 150 feet, which, divided by 12, gives 13 feet as the amount to be deducted from 491 feet, making instead 478 feet, as the degree of declination.
Many have urged that refraction would account for much of the elevation of objects seen at the distance of several miles. Indeed, attempts have been made to show that the large flag at the end of six miles of the Bedford Canal (Experiment 1, fig. 2, p. 13) has been brought into the line of sight entirely by refraction. That the line of sight was not a right line, but curved over the convex surface of the water; and the well-known appearance of an object in a basin of water, has been referred to in illustration. A very little reflection, however, will show that the cases are not parallel; for instance, if the object (a shilling or other coin) is placed in a basin without water there is no refraction. Being surrounded with atmospheric air only, and the observer being in the same medium, there is no bending or refraction of the eye line. Nor would there be any refraction if the object and the observer were both surrounded with water. Refraction
can only exist when the medium surrounding the observer is different to that in which the object is placed. As long as the shilling in the basin is surrounded with air, and the observer is in the same air, there is no refraction; but whilst the observer remains in the air, and the shilling is placed in water, refraction exists. This illustration does not apply to the experiments made on the Bedford Canal, because the flag and the boats were in the same medium as the observer--both were in the air. To make the cases parallel, the flag or the boat should have been in the water, and the observer in the air; as it was not so, the illustration fails. There is no doubt, however, that it is possible for the atmosphere to have different temperature and density at two stations six miles apart; and some degree of refraction would thence result; but on several occasions the following steps were taken to ascertain whether any such differences existed. Two barometers, two thermometers, and two hygrometers, were obtained, each two being of the same make, and reading exactly alike. On a given day, at twelve o'clock, all the instruments were carefully examined, and both of each kind were found to stand at the same point or figure: the two, barometers showed the same density; the two thermometers the same temperature; and the two hygrometers the same degree of moisture in the air. One of each kind was then taken to the opposite station, and at three o'clock each instrument was carefully examined, and the readings recorded, and the observation to the flag, &c., then immediately taken. In a short time afterwards the two sets of observers met each other about midway on the northern
bank of the canal, when the notes were compared, and found to be precisely alike--the temperature, density, and moisture of the air did not differ at the two stations at the time the experiment with the telescope and flag-staff was made. Hence it was concluded that refraction had not played any part in the observation, and could not be allowed for, nor permitted to influence, in any way whatever, the general result.
In 1851, the author delivered a course of lectures in the Mechanics' Institute, and afterwards at the Rotunda, in Dublin, when great interest was manifested by large audiences; and he was challenged to a repetition of some of his experiments--to be carried out in the neighbourhood. Among others, the following was made, across the Bay of Dublin. On the pier, at Kingstown Harbour, a good theodolite was fixed, at a given altitude, and directed to a flag which, earlier in the day, had been fixed at the base of the Hill of Howth, on the northern side of the bay. An observation was made at a given hour, and arrangements had been made for thermometers, barometers, and hygrometers--two of each--which had been previously compared, to be read simultaneously, one at each station. On the persons in charge of the instruments afterwards meeting, and comparing notes, it was found that the temperature, pressure, and moisture of the air had been alike at the two points, at the time the observation was made from Kingstown Pier. It had also been found by the observers that the point observed on the Hill of Howth had precisely the same altitude as that of the theodolite on the pier, and that, therefore, there was no
curvature or convexity in the water across Dublin Bay. It was, of course, inadmissible that the similarity of altitude at the two places was the result of refraction, because there was no difference in the condition of the atmosphere at the moment of observation.
The following remarks from the Encyclopædia Brittanica--article, "Levelling"--bear on the question:--
"We suppose the visual ray to be a straight line, whereas on account of the unequal densities of the air at different distances from the earth, the rays of light are incurvated by refraction. The effect of this is to lessen the difference between the true and apparent levels, but in such an extremely variable and uncertain manner that if any constant or fixed allowance is made for it in formula or tables, it will often lead to a greater error than what it was intended to obviate. For though the refraction may at a mean compensate for about one-seventh of the curvature of the earth, it sometimes exceeds one-fifth, and at other times does not amount to one-fifteenth. We have, therefore, made no allowance for refraction in the foregone formulæ."
It will be seen from the above that, in practice, refraction need not be allowed for. It can only exist when the line of "sight passes from one medium into another of different density; or where the same medium differs at the point of observation and the point observed. If we allow for the amount of refraction which the ordnance surveyors have adopted, viz., one-twelfth of the altitude of the object observed, and apply it to the various experiments made on the Old Bedford Canal, it will make very little difference in the actual results. In the experiment, fig. 3 for
instance, where the top of the flag on the boat should have been 11 feet 8 inches below the horizon, deducting one-twelfth for refraction, would only reduce it to a few inches less than 10 feet.
Others, not being able to deny the fact that the surface of the water in the Old Bedford and other canals is horizontal, have thought that a solution of the difficulty was to be found in supposing the canal to be a kind of "trough" cut into the surface of the earth; and have considered that although the earth is a globe, such a canal or "trough" might exist on its surface as a chord of the arc terminating at each end. This, however, could only be possible if the earth were motionless. But the theory which demands rotundity of the earth also requires rotary motion, and this produces centrifugal force. Therefore the centrifugal action of the revolving earth would, of necessity, throw the waters of the surface away from the centre. This action being equal .at equal distances, and being retarded by the attraction of gravitation (which the theory includes), which is also equal at equal distances, the surface of every distinct and entire mass of water must stand equi-distant from the earth's centre, and, therefore, must be convex, or an arc of a circle. Equi-distant from a centre means, in a scientific sense, "level." Hence the necessity for using the term horizontal to distinguish between "level" and "straight."
29:1 "Lighthouses of the World." Laurie, 53, Fleet Street, London, 1862. Page 9.
29:2 By all the figures given is meant "The minimum distance to which the light can be seen in clear weather from a height of 10 feet above the sea level." Ibid., p. 32.
