MEASUREMENT OF THE EARTH 
107 
j respectively 
Rese loci and 
at a distance 
eometric and 
lie ‘loci with 
two loci are 
:ss to say, we 
\rth. 
\ Eratosthenes 
3 mentions, as 
it the circum- 
s. This was 
ions made at 
was observed 
Ran, the head 
Cancer in the 
ating the two 
nnplete circle, 
re two towns 
3 stades, and 
cumfereuce of 
1 at 300,000 
roved on this, 
at Syene, at 
’ solstice, the 
n an upright 
irmed by the 
dug at the 
lighted up at 
gnomon fixed 
meridian with 
} between the 
plete circle or 
assumed to be 
and A in the 
the sun’s rays 
s also equal to 
a, or 1 / 50th of four right angles. Now the distance from S 
to A was known by measurement to be 5,000 stades; it 
followed tha.t the circumference of the earth was 250,000 
stades. This is the figure given by Cleomedes, but Theon of 
Smyrna and Strabo both give it as 252,000 stades. The 
reason of the discrepancy is not known; it is possible that 
Eratosthenes corrected 250,000 to 252,000 for some reason, 
perhaps in order to get a figure divisible by 60 and, inci 
dentally, a round number (700) of stades for one degree. If 
Pliny is right in saying that Eratosthenes made 40 stades 
equal to the Egyptian a^oivos, then, taking the at 
12,000 Royal cubits of 0-525 metres, we get 300 such cubits, 
or 157-5 metres, i.e. 516-73 feet, as the length of the stade. 
On this basis 252,000 stades works out to 24,662 miles, and 
the diameter of the earth to about 7,850 miles, only 50 miles 
shorter than the true polar diameter, a surprisingly close 
approximation, however much it owes to happy accidents 
in the calculation. 
We learn from Heron’s Dioptra that the measurement of 
the earth by Eratosthenes was given in a separate work On 
the Measurement of the Earth. According to Galen 1 this work 
dealt generally with astronomical or mathematical geography, 
treating of ‘ the size of the equator, the distance of the tropic 
and polar circles, the extent of the polar zone, the size and 
distance of the sun and moon, total and partial eclipses of 
these heavenly bodies, changes in the length of the day 
according to the different latitudes and seasons’. Several 
details are preserved elsewhere of results obtained by 
Eratosthenes, which were doubtless contained in this work. 
He is supposed to have estimated the distance between the 
tropic circles or twice the obliquity of the ecliptic at 11 / 83rds 
of a complete circle or 47° 42 r 39"; but from Ptolemy’s 
language on phis subject it is not clear that this estimate was 
not Ptolemy’s own. What Ptolemy says is that he himself 
found the distance between the tropic circles to lie always 
between 47° 40' and 47° 45', ‘from which we obtain about 
{a-\e86v) the same ratio as that of Eratosthenes, which 
Hipparchus also used. For the distance between the tropics 
becomes (or is found to he, yiverai) very nearly 11 parts 
Galen, Instit. Loyica, 12 (p. 26 Kalbfleisch).