MEASURING THE EARTH--ERATOSTHENES
All told, the Greek philosophers were probably the keenest minds that
ever inhabited the planet, and we cannot suppose them so stupid as to
reject the doctrine of a spherical earth. In fact so certain were they
that the earth's true figure is a sphere that Eratosthenes in the third
century B. C. made the first measure of the dimensions of the
terrestrial sphere by a method geometrically exact.
At Syene in Upper Egypt the sun at the summer solstice was known to pass
through the zenith at noon, whereas at Alexandria Eratosthenes estimated
its distance as seven degrees from the zenith at the same time. This
difference being about one-fiftieth of the entire circumference of a
meridian, Eratosthenes correctly inferred that the distance between
Alexandria and Syene must be one-fiftieth of the earth's circumference.
So he measured the distance between the two and found it 5,000 stadia.
This figured out the size of the earth with a percentage of error
surprisingly small when we consider the rough means with which
Eratosthenes measured the sun's zenith distance and the distance between
the two stations.
Greatest of all the Greek astronomers and one of the greatest in the
history of the science was Hipparchus who had an observatory at Rhodes
in the middle of the second century B. C. His activities covered every
department of astronomy; he made extensive series of observations which
he diligently compared with those handed down to him by the earlier
astronomers, especially Aristillus and Timocharis. This enabled him to
ascertain the motion of the equinoxial points, and his value of the
constant of precession of the equinoxes is exceedingly accurate for a
first determination.
In 134 B. C. a new star blazed out in the constellation Scorpio, and
this set Hipparchus at work on a catalogue of the brighter stars of the
firmament, a monumental work of true scientific conception, because it
would enable the astronomers of future generations to ascertain what
changes, if any, were taking place in the stellar universe. There were
1,080 stars in his catalogue, and he referred their positions to the
ecliptic and the equinoxes. Also he originated the present system of
stellar magnitudes or orders of brightness, and his catalogue was in use
as a standard for many centuries.
Hipparchus was a great mathematician as well, and he devoted himself to
the improvement of the method of applying numerical calculations to
geometrical figures: trigonometry, both plane and spherical, that is;
and by some authorities he is regarded as the inventor of original
methods in trigonometry. The system of spheres of Eudoxus did not
satisfy him, so he devised a method of representing the paths of the
heavenly bodies by perfectly uniform motion in circles. There is slight
evidence that Apollonius of Perga may have been the originator of the
system, but it was reserved for Hipparchus to work it out in final form.
This enabled him to ascertain the varying length of the seasons, and he
fixed the true length of the year as 365-1/4 days. He had almost equal
success in dealing with the irregularities of the moon's motion,
although the problem is much more complicated. The distance and size of
the moon, by the method of Aristarchus, were improved by him, and he
worked out, for the distance of the sun, 1,200 radii of the earth--a
classic for many centuries.
Hipparchus devoted much attention to eclipses of both sun and moon, and
we owe to him the first elucidation of the subject of parallax, or the
effect of difference of position of an observer on the earth's surface
as affecting the apparent projection of the moon against the sun when a
solar eclipse takes place; whereas an eclipse of the moon is unaffected
by parallax and can be seen at the same time by observers everywhere, no
matter what their location on the earth. Indeed, with all that
Hipparchus achieved, we need not be surprised that astronomy was
regarded as a finished science, and made practically no progress
whatever for centuries after his time.
Then came Claudius Ptolemaeus, generally known as Ptolemy, the last great
name in Greek astronomy. He lived in Alexandria about the middle of the
second century A. D. and wrote many minor astronomical and astrological
treatises, also works on geography and optics, in the last of which the
atmospheric refraction of rays of light from the heavenly bodies,
apparently elevating them toward the zenith, is first dealt with in true
form.