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.