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.