524 
Equally important, also, in its far reach- 
ing connections was the work of Hratos- 
thenes in determining the size of the earth. 
This work required an hypothesis as to the 
shape of the earth and appropriate obser- 
vations. Supposing the earth to be spher- 
ical, an assumption which Eratosthenes 
knew well how to justify, he saw that to 
determine its size it is only necessary to 
apply the rule of three to the measured 
length of an arc of a meridian and to the 
measured difference of the latitudes of the 
ends of such arc. He observed that at the 
city of Syene, which is about 500 miles 
south of Alexandria, the sun shone verti- 
cally downwards into deep wells at noon 
on the day of the summer solstice, showing 
thus that at that place and time the sun 
was in the zenith. On the same day at 
Alexandria he observed, by means of the 
gnomon, that the sun at noon was south of 
the zenith by one-fiftieth of a circle, or 7°.2. 
The distance between the two points was 
found by the royal road masters of the 
country to be 5,000 stadia, thus giving for 
the complete circumference of the earth 
250,000 stadia. Although the measure- 
ments thus made by Eratosthenes were 
very crude and undoubtedly subject to 
large errors, we see in them the beginnings 
of some of the most refined geodetic oper- 
ations of the present day. Unfortunately 
for us, also, the measurement of the dis- 
tance is expressed in a unit whose relation 
to modern units is only roughly known.* 
But commendable as was the work of his 
predecessors and contemporaries, the work 
* As illustrating the slow growth of ideas with re_ 
spect to precision, it may be related that when the 
Arabians in the ninth century undertook, for the 
same purpose, the measurement of a meridional are 
on the plain of Singiar, in Mesopotamia, they were 
not more successful in preserving for posterity the 
standard of length used by them. This standard is 
said to have been the ‘ black cubit, which consists of 
27 inches, each inch being the thickness of six grains 
of barley.’ 
SCIENCE. 
[N. S. Vou. XIII. No. 327. 
of Hipparchus rises to a still higher plane. 
He was an observer and a theorist of the 
highest type, being able at once to collect 
facts and to interpret their relations, and 
he deserves to be ranked among the great 
astronomers of all times. He was the first 
to clearly appreciate the value of a cata- 
logue of the fixed stars and constructed one 
giving the relative positions of 1,080 stars. 
He observed with surprising precision the 
interval of the tropical year; he made the 
first tables of the sun and moon; he dis- 
covered the remarkable fact of the preces- 
sion of the equinoxes, and he thus early 
led the way to the great advances of modern 
times. 
The peculiar merit of the work of Hip- 
parchus lies not alone in the fact that he 
saw how the apparent motions of the 
heavenly bodies may be determined by ob- 
servations, but also in the fact that he saw 
how these motions may be determined by a 
very small number of appropriate observa- 
tions. Thus, for example, the interval from 
tbe vernal equinox to the summer solstice 
and the interval from the latter to the 
autumnal equinox sufficed to give him a 
close approximation to the apparent motion 
of the sun; while the records of a few 
eclipses of the moon enabled him to deduce 
a closely correct value of the precession of 
the equinoxes, that shifting of the line of 
intersection of the equator and the ecliptic 
which goes on so slowly that an interval of 
nearly 26,000 years is required for a com- 
plete circuit. 
Hipparchus may be called the founder of 
the geocentric theory, since he demonstrated 
the accordance of the phenomena known to 
him with that theory. The fact that this 
theory is false detracts little from his merits ; 
for the sole requisites of a good theory are 
simplicity of statement and conformity with 
observation. We now know, indeed, that 
mechanical phenomena are, in general, sus- 
ceptible of multiple interpretations, and that 
