252 
PRESTON. 
ances, passed successively through the belief in a flat disc, a 
sphere, an ellipsoid, and a geoid, and finally, as observations 
became more and more exact and the requirements of theory 
demanded that new conditions should be satisfied, we have 
passed the stage where any better mean figure can be sup¬ 
plied and a new line of attack must be devised. All our 
future investigations must be limited to the deformations of 
the ellipsoid; and whether they are revealed by the pendu¬ 
lum, by the measurement of arcs, or by whatever process, 
we shall have an accumulation of data from which may be 
deduced a figure of the earth compatible with the known 
laws of nature. The spherical shape of our planet was con¬ 
firmed by the simplest observations. The ellipsoid deduced 
by Newton from purely theoretical considerations was con¬ 
firmed by geodetic measurements in Lapland and Peru, 
and it now seems likely that the tetrahedral shape will be 
sustained by recent measure of parallel arcs. 
Before taking up the tetrahedral theory we shall briefly 
recall a few of the steps in the development of our knowl¬ 
edge of the earth’s figure. The belief in a flat disc dates 
from the Songs of Homer. Notwithstanding the fact that 
the simplest observation on the seashore shows the in¬ 
adequacy of this theory, it continued to prevail for seven 
centuries. Pythagoras then asserted the doctrine of the 
sphere. This, however, was not seriously considered for 300 
years. Then Aristotle took up the question, weighed the 
evidence for and against, and came to the conclusion that 
the disc idea was untenable. Another century passed before 
it occurred to any one to actually measure the earth’s cir¬ 
cumference. Eratosthenes did this by observing at two 
points the direction of the sun’s rays with reference to a 
vertical line. Some one else applied the same principle 100 
years later, using a star and referring the directions to the 
horizon, so that at the beginning of the Christian era it 
was pretty well established that the earth was a sphere, and 
that its diameter was about eleven million meters, as we de¬ 
fine that unit today. The error of a million meters in this 
