Part 3

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_!

An argument for the Earth’s convexity is thought by many to be found in the following facts:--“Fluid or semi-fluid substances in a state of motion invariably assume the globular form, as rain, hail, dew, mercury, and melted lead, which, poured from a great height becomes divided into spherical masses, as in the manufacture of small shot, &c.” “There is abundant evidence from geology that the Earth has been a fluid or semi-fluid mass, and it could not, therefore, continue in a state of motion through space without becoming spherical.” Without denying that the Earth has been, at some former period, in a pulpy or semi-fluid state, it is requisite to prove beyond all doubt that it has a motion upon axes and through space, or the conclusion that it is therefore spherical is premature and illogical. It will be shown in a subsequent part of this work, that such axial and orbital motion does not exist, and therefore any argument founded upon and including it as a fact is necessarily fallacious. In addition to this, it may be remarked that the tendency in falling fluids to become globular is owing to what has been called “attraction of cohesion” (not “attraction of gravitation”), which is very limited in its operation. It is confined to small quantities of matter. If, in the manufacture of small shot, the melted metal is allowed to fall in masses of several ounces or pounds, instead of being divided into particles weighing only a few grains, it will never take a spherical form, and shot of an inch in diameter could not be made by this process. Bullets of even half-an-inch diameter can only be made by casting the metal into spherical moulds. In tropical countries, the rain instead of falling in drops or small globules, often comes down in large irregular masses, which have no approximation whatever to sphericity. So that it is manifestly unjust to affirm of large masses of matter like the Earth that which only belongs to minute portions or a few grains in weight. The whole matter taken together entirely fails as an argument for the Earth’s rotundity.

Those who hold that the Earth is a globe will often affirm, with visible enthusiasm, that in an eclipse of the Moon there is proof positive of rotundity. That the shadow of the Earth upon the Moon is always round; and that nothing but a globe could, in all positions, cast a circular shadow. Here again the essential requirements of an argument are wanting. It is _not proved_ that the Moon is eclipsed _by a shadow_. It is _not proved_ that the _Earth moves_ in an orbit, and therefore takes _different positions_. It is _not proved_ that the Moon receives her light from the Sun, and that therefore her surface is darkened by the Earth intercepting the Sun’s light. It will be shown in the proper place that the Earth has no motion in space or on axes; that it is not a shadow which eclipses the Moon; that the Moon is not a reflector of the Sun’s light, but is _self-luminous_; and therefore could not possibly be obscured by _a shadow_ from any object whatever. The subject is only introduced here because it forms one of the category of supposed evidences of the Earth’s rotundity. But to call that an argument where every necessary proposition is assumed, is to stultify both the judgment and the reasoning powers!

Many place great reliance upon what is called the “spherical excess” observed in levelling, as a proof of the Earth’s rotundity. In Castle’s Treatise on Levelling it is stated that “the angles taken between any three points on the surface of the Earth by the theodolite, are, strictly speaking, spherical angles, and their sum must exceed 180 degrees; and the lines bounding them are not the chords as they should be, but the tangents to the Earth. This excess is inappreciable in common cases, but in the larger triangles it becomes necessary to allow for it, and to diminish each of the angles of the observed triangle by one-third of the spherical excess. To calculate this excess, divide the area of the triangle in feet by the radius of the Earth in seconds and the quotient is the excess.”