The Progress of the Century

by Unknown

INVESTIGATIONS OF SOME IMPORTANT ASTRONOMICAL CONSTANTS

The nineteenth century was fruitful in the determination of many numerical values which are all important in enabling us to determine the distance and masses of the heavenly bodies, thereby giving us a firm grasp not only of the dimensions of our own system, but of those scattered in the celestial spaces.

To take the distances first. We must begin with the exact measure of the earth; for this we must measure the exact length of an arc of meridian or of parallel—that is, a stretch of the earth’s surface lying north and south or east and west, between places of which the latitudes are accurately known in the former case, and the longitude in the latter. In either case we can determine the number of miles which go to a degree. Beginning at the opening of the nineteenth century with an arc of meridian of two degrees measured by Gauss, from Göttingen to Altona, the arcs of meridian grew longer as the century grew older, till, at the close, the measurement of an arc of meridian from the Cape to Cairo, embracing something like sixty-eight degrees of latitude, was mooted.

The measurements of arcs of parallel have been developed by the rapid extension of telegraphic communications, which now permit the longitude of the terminal stations to be determined with the greatest accuracy.

Thanks to this work, we now have the size of our planet to a few miles. The polar diameter is 41,709,790 feet, but the equator is not a circle: the equatorial diameter from longitude 8 degrees 15 minutes west to longitude 188 degrees 15 minutes west is 41,853,258 feet; that at right angles to it is 41,850,210 feet—that is, some thousand yards shorter. The earth, then, is shaped like an orange slightly squeezed.

Knowing the earth’s diameter, we can obtain the sun’s distance by several methods, the old one by observing transits of Venus, one of which Cook went out to observe in 1768, and two of which recurred in 1874 and 1882; new ones by observations of Mars or one of the minor planets at a favorable opposition, and by determining the velocity of light.

The recent discovery of a minor planet, Eros, which in one part of its orbit is nearer the earth than Mars, has recently revived interest in this method, and a combined attack is in contemplation.

It has been long known that light has a finite velocity, but we had to wait till the 60’s before Fizeau and Foucault showed us how to determine its exact value. The methods introduced by them have been recently applied by Cornu, Newcomb, and Michelson, and the resulting value is slightly less than three hundred thousand metres per second. Combining this with the constant of aberration, the distance of the sun can be determined.

It is wonderful how these vastly different methods agree in the resulting mean distance. At the beginning of the century it stood roughly at ninety-five million miles; this has been reduced to ninety-three million nine hundred and sixty-five thousand miles. The extreme difference between the old and new values of the solar parallax, two-fifths of a second of arc, is represented by the apparent breadth of a human hair viewed at a distance of about one hundred and twenty-five feet.

Knowing the distance of the sun, the way is open to us to determine, by a method suggested by Galileo, the distances of those stars which occupy a different position among their fellows, as seen from opposite points in the earth’s orbit round the sun, points one hundred and eighty-six million miles apart. We now know the distances of many such stars, Bessel having determined the first in 1838. The nearest star to us, so far as we know, is Centauri, the light of which takes four and a half years to reach us. Not many years ago Pritchard applied photography to this branch of inquiry; we may, therefore, expect a still more rapid progress in the future.

With regard to masses. We naturally must first know that of the earth; having its size, if we can determine its density, the rest follows.

The problem of determining the mean density of the earth occupied the minds of many workers during the nineteenth century. Newton (about 1728) pointed out how it could be deduced by observing the deviation from the vertical of a plumb-line suspended near a large mass of matter—a mountain, the volume and density of which could be previously determined. This method, which is very laborious and requires the greatest skill and most delicate instruments, has been employed several times, by Bouguer and Condamine, in 1738, at Chimborazo; Maskelyne, in 1774, at Schehallien in Scotland; and James, at Arthur’s Seat, near Edinburgh.

At the beginning of the century another method was introduced by Cavendish. This consists in measuring the attraction of two large spheres of known size and mass, such as two balls of lead on two very small and light spheres, by means of a torsion balance constructed by Mitchell for this purpose.

The most recent determination by this method, and one which is considered to give us perhaps the most accurate value, is that which is due to the skill and ingenuity of Professor Boys. His improvement consisted in constructing a most delicate torsion balance; the attracted spheres consisted of small gold balls suspended by a quartz fibre carrying a mirror to indicate the amount of twist. The whole instrument was quite small, and could easily be protected from air currents and changes of temperature, while the use of the quartz fibres reduced to a minimum one of the greatest difficulties of the Cavendish experiment. The value of the mean density of the earth is now considered to be 5.6, which means that if we have a globe of water exactly the same size as our own earth, the real earth would weigh just 5.6 times this globe of water. The earth’s weight, in tons, does not convey much idea, but that it is six thousand trillions may interest the curious. This determination has enabled the masses of the sun, moon, planets and satellites, and many sidereal systems to be accurately known in relation to the mass of the earth.