Part 3
In further illustration of this matter, and to impress the mind of the readers with its importance as an evidence in support of the theory of the earth’s sphericity, several authors have given the following story:--Two brothers, twins, born within a few minutes of each other, and therefore of the same age, on growing to manhood went to sea. They both circumnavigated the earth, but in opposite directions; and when they again met, one was a day older than the other!
Whatever truth there may be in this account, it is here shown to be no more favourable to the idea of rotundity than it is to the opposite fact that the earth is a plane; as both forms will permit of the same effect.
Another phenomenon supposed to prove rotundity, is found in the fact that Polaris, or the north polar star, gradually sinks to the horizon as the mariner approaches the equator, on passing which it becomes invisible. First, it is an ordinary effect of perspective for an object to appear lower and lower as the observer recedes. Let any one try the experiment of looking at a lighthouse, church spire, monument, gas-lamp, or other elevated object, from the distance of a few yards, and notice the angle at which it is observed: on going farther away, the angle will diminish and the object appear lower, until, if the distance be sufficiently great, the line-of-sight to the object, and the apparently ascending surface of the Earth upon which it stands will converge to the angle which constitutes the vanishing point; at a single yard beyond which it will be invisible. This, then, is the necessary result of the everywhere visible law of perspective operating between the eye-line and the plane surface upon which the object stands; and has no relation whatever to rotundity.
It is not denied that a similar depression of a distant object would take place upon a globe; it is simply contended that it would not occur upon a globe exclusively. But if the Earth is a sphere and the pole star hangs over the northern axis, it would be impossible to see it for a single degree beyond the equator, or 90 degrees from the pole. The line-of-sight would become a tangent to the sphere, and consequently several thousand miles out of and divergent from the direction of the pole-star. Many cases, however, are on record of the north polar star being visible far beyond the equator, as far even as the tropic of Capricorn. In the _Times_ newspaper of May 13, 1862, under the head of “Naval and Military Intelligence,” it is stated that Captain Wilkins distinctly saw the Southern Cross and the polar star at midnight in 23·53 degrees of latitude, and longitude 35·46.
[Illustration: FIG. 20.]
This would be utterly impossible if the Earth were a globe, as shown in the diagram, Figure 20. Let N represent the north pole, E E the equator, C C the tropic of Capricorn, and P the polar star. It will be evident that the line-of-sight C D being a tangent to the Earth beyond the equator E must diverge from the axis N and could not by any known possibility cause the star P to be visible to an observer at C. No matter how distant the star P, the line C D being divergent from the direction N P could never come in contact with it. The fact, then, that the polar star has often been seen from many degrees beyond the equator, is really an important argument against the doctrine of the Earth’s rotundity.
It has been thought that because a pendulum vibrates more rapidly in the northern region than at the equator, the Earth is thereby proved to be a globe; and because the variation in the velocity is not exactly as it should be if all the surface of the Earth were equidistant from the centre, it has been concluded that the Earth is an oblate spheroid, or that its diameter is rather less through the poles than it is through the equator. The difference was calculated by Newton to be the 235th part of the whole diameter; or that the polar was to the equatorial diameter as 689 to 692. Huygens gave the proportion as 577 to 875 or a difference of about one-third of the whole diameter. Others have given still different proportions; but recently the difference of opinion has become so great that many have concluded that the Earth is really instead of oblate an _oblong_ spheroid. It is certain that the question when attempted to be answered by measuring arcs of the meridian, is less satisfactory than was expected. This will be evident from the following quotation from the account of the ordnance survey of Great Britain, which was conducted by the Duke of Richmond, Col. Mudge, General Roy, Mr. Dalby, and others, who measured base lines on Hounslow Heath and Salisbury Plain with glass rods and steel chains: “when these were connected by a chain of triangles and the length computed the result did not differ more than one inch from the actual measurements--a convincing proof of the accuracy with which all the operations had been conducted.
The two stations, of Beachy Head in Sussex and Dunnose in the Isle of Wight, are visible from each other, and more than 64 miles asunder, nearly in a direction from east to west; their exact distance was found by the geodetical operations to be 339,397 feet (64 miles and 1477 feet). The azimuth, or bearing of the line between them with respect to the meridian, and also the latitude of Beachy Head, were determined by astronomical observations. From these data the length of a degree perpendicular to the meridian was computed; and this, compared with the length of a meridional degree in the same latitude, gave the proportion of the polar to the equatorial axis. The result thus obtained, however, differed considerably from that obtained by meridional degrees. It has been found impossible to explain the want of agreement in a satisfactory way. * * By comparing the celestial with the terrestrial arcs, the length of degrees in various parallels was determined as in the following table:--
Latitude of middle point. Fathoms. ° ′ ″ Arbury Hill and Clifton 52 50 29·8 60,766 Blenheim and Clifton 52 38 56·1 60,769 Greenwich and Clifton 52 28 5·7 60,794 Dunnose and Clifton 52 2 19·8 60,820 Arbury Hill and Greenwich 51 51 4·1 60,849 Dunnose and Arbury Hill 51 35 18·2 60,864 Blenheim and Dunnose 51 13 18·2 60,890 Dunnose and Greenwich 51 2 54·2 60,884
This table presents a singular deviation from the common rule; for instead of the degrees _increasing_ as we proceed from north to south, they appear to _decrease_, as if the Earth were an _oblong_ instead of an _oblate_ spheroid. * * The measurements of small arcs of the meridian in other countries have presented similar instances.”[4]
[4] Encyclopedia of Geography, by Hugh Murray and several Professors in the University of Edinburgh.
A number of French Academicians who measured above three degrees of the meridian in Peru, gave as the result of their labours the first degree of the meridian from the equator as 56,653 toises; whilst another company of Academicians, who proceeded to Bothnia in Lapland, gave as the result of their calculation 57,422 toises for the length of a degree cutting the polar circle. But a more recent measurement made by the Swedish Astronomers in Bothnia shows the French to have been incorrect, having given the degree there 196 toises more than the true length. Other observations have been made, but as no two sets of experiments agree in result, it would be very unsatisfactory to conclude from them that the Earth is an oblate spheroid.
Returning to the pendulum, it will be found to be equally unsatisfactory as a proof of this peculiar rotundity of the Earth. It is argued that as the length of a seconds pendulum at the equator is 39,027 inches, and 39,197 inches at the north pole, that the Earth must be a globe, having a less diameter through its axis than through its equator. But this proceeds upon the _assumption_ that the Earth _is_ a globe having a “centre of attraction of gravitation,” towards which all bodies gravitate or fall; and as the pendulum is a falling body under certain restraint, the fact that it oscillates or falls more rapidly at the north than it does at the equator, is a proof that the north is nearer to the centre of attraction, or the centre of the Earth, than is the equatorial region; and, of course, if nearer, the radius must be shorter; and therefore the “Earth is a spheroid flattened at the poles.” This is very ingenious and very plausible, but, unfortunately for its character as an argument, the essential evidence is wanting that the Earth is a globe at all! whether oblate or oblong, or truly spherical, are questions logically misplaced. It should also be first proved that _no other_ cause could operate besides greater proximity to the centre of gravity, to produce the variable oscillations of a pendulum. This not being attempted, the whole subject must be condemned as logically insufficient, irregular, and worthless for its intended purpose. Many philosophers have ascribed the alterations in the oscillations of a pendulum to the diminished temperature of the northern centre. That the heat gradually and almost uniformly diminishes on passing from the equator to the north is well ascertained. “The mean annual temperature of the whole Earth at the level of the sea is 50° Fah. For different latitudes it is as under:--
Degrees. Inches. Latitude (Equator) 0 84·2 Length of Pendulum 39,027 „ „ 10 82·6 „ „ „ „ „ 20 78·1 „ „ „ „ „ 30 71·1 „ „ „ „ „ 40 62·6 „ „ „ „ (London) 50 53·6 „ „ 39,139 „ „ 60 45·0 „ „ „ „ „ 70 38·1 „ „ „ „ „ 80 33·6 „ „ „ „ (Pole) 90 00·0 „ „ 39,197[5]”
[5] “Million of Facts,” by Sir Richard Phillips, p. 475.
“All the solid bodies with which we are surrounded are constantly undergoing changes of bulk corresponding to the variations of temperature. * * The expansion and contraction of metals by heat and cold form subjects of serious and careful attention to chronometer makers, as will appear by the following statements:--The length of the pendulum vibrating seconds, in vacuo, in the latitude of London (51° 31′ 8″ north), at the level of the sea, and at the temperature of 62°, has been ascertained with the greatest precision to be 39·13929 inches: now, as the metal of which it is composed is constantly subject to variation of temperature, it cannot but happen that its _length_ is constantly varying; and when it is further stated that if the “bob” be let down ¹⁄₁₀₀th of an inch, the clock will lose 10 seconds in 24 hours; that the elongation of ¹⁄₁₀₀₀th of an inch will cause it to lose one second per day; and that a change of temperature equal to 30° Fah. will alter its length ¹⁄₅₀₀₀th part and occasion an error in the rate of going of 8 seconds per day, it will appear evident that some plan must be devised for obviating so serious an inconvenience.”[6]
[6] “Noad’s Lectures on Chemistry,” p. 41.
From these data it is readily seen that the variations in the rate of a pendulum as it is carried from the equator towards the north are sufficiently explained, without supposing that they arise from a peculiar spheroidal form of the Earth.
Others have attributed the variable motions of the pendulum to increased density of the air on going northwards. That the condition of the air must have some influence in this respect will be seen from the following extract from experiments on pendulums by Dr. Derham, recorded in numbers 294 and 480 of the _Philosophical Transactions_:--“The arches of vibration _in vacuo_ were larger than in the open air, or in the receiver before it was exhausted; the enlargement or diminution of the arches of vibration were _constantly proportional_ to the _quantity of air_, or rarity, or density of it, which was left in the receiver of the air-pump. And as the _vibrations_ were _longer_ or _shorter_, _so_ the _times_ were accordingly, viz., two seconds in an hour when the vibrations were longest, and less and less as the air was re-admitted, and the vibrations shortened.”
Thus there are two distinct and tangible causes which necessarily operate to produce the variable oscillations of a pendulum, without supposing any distortion in the supposed rotundity of the Earth. First, if the pendulum vibrates in the air, which is colder and therefore denser in the north than at the equator, it must be more or less resisted in its passage through it; and, secondly, if it vibrates _in vacuo_, the temperature being less, the length must be less, the arcs of vibration less, and the velocity greater. In going towards the equator, the temperature increases, the length becomes greater, the arcs increase, and the times of vibration diminish.
Another argument for the globular form of the Earth is the following:--The degrees of longitude radiating from the north pole gradually increase in extent as they approach the equator; beyond which they again converge towards the south. To this it is replied that no actual measurement of a degree of longitude has ever been made south of the equator! If it be said that mariners have sailed round the world in the southern region and have _computed_ the length of the degrees, it is again replied that such evidence is unfavourable to the doctrine of rotundity. It will be seen from the following table of what the degrees of longitude would be if the earth were a globe of 25,000 miles circumference, and comparing these with the results of practical navigation, that the diminution of degrees of longitude beyond the equator is purely imaginary.
Latitudes at different longitudes:--
Latitude 1 = 59·99 nautical miles. 10 = 59·09 „ „ 20 = 56·38 „ „ 30 = 51·96 „ „ 34 = 49·74 (Cape Town) 40 = 45·96 „ „ 45 = 42·45 (Port Jackson, Sydney) 50 = 38·57 „ „ 56 = 33·55 (Cape Horn) 60 = 30·00 „ „ 65 = 25·36 „ „ 70 = 20·52 „ „ 75 = 15·53 „ „ 80 = 10·42 „ „ 85 = 5·53 „ „ 86 = 4·19 „ „ 87 = 3·14 „ „ 88 = 2·09 „ „ 89 = 1·05 „ „ 90 = 0·00 „ „
According to the above table (which is copied from a large Mercator’s chart in the library of the Mechanics’ Institute, Royal Hill, Greenwich), the distance round the Earth at the Antarctic circle would only be about 9,000 miles. But practical navigators give the distance from the Cape of Good Hope to Port Jackson as 8,000 miles; from Port Jackson to Cape Horn as 8,000 miles; and from Cape Horn to the Cape of Good Hope, 6,000 miles, making together 22,000 miles. The average longitude of these places is 45°, at which parallel the circuit of the Earth, if it be a globe, should only be 14,282 miles. Here, then, is an error between the theory of rotundity and practical sailing of 7,718 miles. But there are several statements made by Sir James Clarke Ross which tend to make the disparity even greater: at page 236, vol. 2, of “South Sea Voyages,” it is said “From near Cape Horn to Port Philip (in Melbourne, Australia) the distance is 9,000 miles.” These two places are 143 degrees of longitude from each other. Therefore the whole extent of the Earth’s circumference is a mere arithmetical question. If 143 degrees make 9,000 miles, what will be the distance made by the whole 360 degrees into which the surface is divided? The answer is, 22,657 miles; or, 8,357 miles more than the theory of rotundity would permit. It must be borne in mind, however, that the above distances are nautical measure, which, reduced to statute miles, gives the actual distance round the Southern region at a given latitude as 26,433 statute miles; or nearly 1,500 miles more than the largest circumference ever assigned to the Earth at the equator.
But actual measurement of a degree of longitude in Australia or some other land far south of the equator can alone place this matter beyond dispute. The problem to be solved might be given as the following:--A degree of longitude in England at the latitude of 50° N. is 38·57 nautical or 45 statute miles; at the latitude of Port Jackson in Australia, which is 45° S., a degree of longitude, if the Earth is a globe, should be 42·45 nautical or 49·52 statute miles. But if the Earth is a plane, and the distances above referred to as given by nautical men are correct, a degree of longitude on the parallel of Port Jackson will be 69·44 statute miles, being a difference of 19·92 or nearly 20 statute miles. In other words, a degree of longitude along the southern part of Australia ought to be, _if the Earth is a plane_, nearly 20 miles greater than a degree of longitude on the southern coast of England. This is the point which has yet to be settled. The day is surely not far distant when the scientific world will demand that the question be decided by proper geodetical operations! And this not altogether for the sake of determining the true figure of the Earth, but also for the purpose of ascertaining, if possible, the cause of the many anomalies observed in navigating the southern region. These anomalies have led to the loss of many vessels and the sacrifice of a fearful amount of life and property. “In the southern hemisphere, navigators to India have often fancied themselves east of the Cape when still West, and have been driven ashore on the African coast, which according to their reckoning lay behind them. This misfortune happened to a fine frigate, the “Challenger,” in 1845.”[7] “Assuredly there are many shipwrecks from alleged errors in reckoning which _may_ arise from a somewhat false idea of the general form and measurement of the Earth’s surface. Such a subject, therefore, ought to be candidly and boldly discussed.”[8]
[7] “Tour through Creation,” by the Rev. Thomas Milner, M.A.
[8] “The Builder,” Sept. 20, 1862, in a “review” of a recently-published work on Astronomy.
It is commonly believed that surveyors when laying out railways and canals, are obliged to allow 8 inches per mile for the Earth’s curvature; and that if this were not done in the latter case the water would not be stationary, but would flow on until at the end of one mile in each direction, although the canal should have the same depth throughout, the surface would stand 8 inches higher in the middle than at the ends. In other words, that the bottom of a canal in which the allowance of 8 inches per mile had not been made, would be a chord to the surface of the contained water, which would be an arc of a circle. To this it is replied, that both in regard to railways and canals, wherever an allowance has been attempted the work has not been satisfactory; and so irregular were the results in the earlier days of railway, canal, and other surveying, that, the most eminent engineers abandoned the practice of the old “forward levelling” and allowing for convexity; and adopted what is now called the “double sight” or “back-and-fore sight” method. It was considered that whether the surface were convex or horizontal, or whether the convexity were more or less than the supposed degree, would be of no consequence in practice if the spirit level or theodolite were employed to read both backwards and forwards; for whatever degree of convexity existed, one “sight” would compensate for the other; and if the surface were horizontal, the same mode of levelling would apply. So important did the ordnance department of the Government consider this matter, that it was deemed necessary to make the abandonment of all ideas of rotundity compulsory, and in a standing order (No. 6) of the House of Lords as to the preparation of sections for railways, &c., the following language is used, “That the section be drawn to the same _horizontal_ scale as the plan; and to a vertical scale of not less than one inch to every one hundred feet; and shall show the surface of the ground marked on the plan, the intended level of the proposed work, the height of every embankment, and the depth of every cutting; and a _datum_ HORIZONTAL LINE, which shall be _the same throughout the whole length of the work_, or any branch thereof respectively; and shall be referred to some fixed point stated in writing on the section, near some portion of such work; and in the case of a canal, cut, navigation, turnpike, or other carriage road, or railway, near either of the termini.” No. 44 of the standing orders of the House of Commons is similar to the above order (No. 6) of the House of Lords.
Thus it is evident that the doctrine of the Earth’s rotundity cannot be mixed up with the practical operations of civil engineers and surveyors, and to prevent the waste of time and the destruction of property which necessarily followed the doings of some who were determined to involve the convexity of the Earth’s surface in their calculations, the very Government of the country has been obliged to interfere! Every survey of this and other countries, whether ordnance or otherwise, is now carried out in connection with a horizontal datum, and therefore, as no other method proves satisfactory, it is virtually an admission by all the most practical scientific men of the day that the Earth _cannot be other than a plane_!