THE SAND-RECKONER * 
83 
ns as to the 
heir relation 
portunity of 
tys, to prove 
DO stades; in 
jut ten times 
s diameter of 
takes to he 
it of the sun. 
lun to be nine 
twelve times, 
r than 18 but 
will again be 
ot more. The 
i ratio of the 
Here he seizes 
of the fixed 
loses the earth 
portion to the 
phere bears to 
nnatical sense, 
nfinite in size, 
jO get another 
Aristarchus’s 
e centre, being 
ny other mag- 
terpretation of 
we conceive a 
een the centre 
A fixed stars). 
a; Aristarchus 
ihat the size of 
,t of the sphere 
f Archimedes’s 
and, in making 
he was taking 
ving his hypo- 
Archimedes has, lastly, to compare the diameter of the sun 
with the circumference of the circle described by its centre. 
Aristarchus had made the apparent diameter of the sun T -| ff th 
of the said circumference ; Archimedes will prove that the 
said circumference cannot contain as many as 1,000 sun’s 
diameters, or that the diameter of the sun is greater than the 
side of a regular chiliagon inscribed in the circle. First he 
made an experiment of his own to determine the apparent 
diameter of the sun. With a small cylinder or disc in a plane 
at right angles to a long straight stick and moveable along it, 
he observed the sun at the moment when it cleared the 
horizon in rising, moving the disc till it just covered and just 
failed to cover the sun as he looked along the straight stick. 
He thus found the angular diameter to lie between j^R and 
2js-gR, where R is a right angle. But as, under his assump 
tions, the size of the earth is not negligible in comparison with 
the sun’s circle, he had to allow for parallax and find limits 
for the angle subtended by the sun at the centre of the earth. 
This he does by a geometrical argument very much in the 
manner of Aristarchus. 
Let the circles with centres 0, C represent sections of the sun 
and earth respectively, E the position of the observer observing 
g 2