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and Pythagorean deductive dreams about the mysterious powers of
numbers； and of the regular solids。
Such a people； when they took to studying physical science； would be；
and in fact were； incapable of Chemistry； Geognosy； Comparative
Anatomy； or any of that noble choir of sister sciences； which are now
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building up the material as well as the intellectual glory of Britain。
To Astronomy； on the other hand； the pupils of Euclid turned naturally；
as to the science which required the greatest amount of their favourite
geometry： but even that they were content to let pass from its inductive
to its deductive stagenot as we have done now； after two centuries of
inductive search for the true laws； and their final discovery by Kepler and
Newton： but as soon as Hipparchus had propounded any theory which
would do instead of the true laws； content there to stop their experiments；
and return to their favourite work of commenting； deducing； spinning
notion out of notion； ad infinitum。
Still； they were not all of this temper。 Had they been； they would
have discovered； not merely a little； but absolutely nothing。 For after all；
if we will consider； induction being the right path to knowledge； every
man； whether he knows it or not； uses induction； more or less； by the mere
fact of his having a human reason； and knowing anything at all； as M。
Jourdain talked prose all his life without being aware of it。
Aristarchus is principally famous for his attempt to discover the
distance of the sun as compared with that of the moon。 His method was
ingenious enough； but too rough for success； as it depended principally on
the belief that the line bounding the bright part of the moon was an exact
straight line。 The result was of course erroneous。 He concluded that the
sun was 18 times as far as the moon； and not； as we now know； 400； but
his conclusion； like his conception of the vast extent of the sphere of the
fixed stars； was far enough in advance of the popular doctrine to subject
him； according to Plutarch； to a charge of impiety。
Eratosthenes； again； contributed his mite to the treasure of human
sciencehis one mite； and yet by that he is better known than by all the
volumes which he seems to have poured out； on Ethics； Chronology；
Criticism on the Old Attic Comedy； and what not； spun out of his weary
brain during a long life of research and meditation。 They have all
perished；like ninety…nine hundredths of the labours of that great literary
age； and perhaps the world is no poorer for the loss。 But one thing；
which he attempted on a sound and practical philosophic method； stands；
and will stand for ever。 And after all； is not that enough to have lived for？
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to have found out one true thing； and； therefore； one imperishable thing； in
one's life？ If each one of us could but say when he died： 〃This one
thing I have found out； this one thing I have proved to be possible； this
one eternal fact I have rescued from Hela； the realm of the formless and
unknown；〃 how rich one such generation might make the world for ever！
But such is not the appointed method。 The finders are few and far
between； because the true seekers are few and far between； and a whole
generation has often nothing to show for its existence but one solitary gem
which some one manoften unnoticed in his timehas picked up for them；
and so given them 〃a local habitation and a name。〃
Eratosthenes had heard that in Syene； in Upper Egypt； deep wells were
enlightened to the bottom on the day of the summer solstice； and that
vertical objects cast no shadows。
He had before suggested； as is supposed； to Ptolemy Euergetes； to
make him the two great copper armillae； or circles for determining the
equinox； which stood for centuries in 〃that which is called the Square
Porch〃probably somewhere in the Museum。 By these he had calculated
the obliquity of the ecliptic； closely enough to serve for a thousand years
after。 That was one work done。 But what had the Syene shadows to do
with that？ Syene must be under that ecliptic。 On the edge of it。 In short；
just under the tropic。 Now he had ascertained exactly the latitude of one
place on the earth's surface。 He had his known point from whence to
start on a world…journey； and he would use it； he would calculate the
circumference of the earthand he did it。 By observations made at
Alexandria； he ascertained its latitude compared with that of Syene； and so
ascertained what proportion to the whole circumference was borne by the
5000 stadia between Alexandria and Syene。 He fell into an error； by
supposing Alexandria and Syene to be under the same meridians of
longitude： but that did not prevent his arriving at a fair rough result of
252；000 stadia31；500 Roman miles； considerably too much； but still；
before him； I suppose； none knew whether it was 10；000； or 10；000；000。
The right method having once been found； nothing remained but to
employ it more accurately。
One other great merit of Eratosthenes is； that he first raised Geography
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to the rank of a science。 His Geographica were an organic collection； the
first the world had ever seen； of all the travels and books of earth…
description heaped together in the Great Library； of which he was for
many years the keeper。 He began with a geognostic book； touched on the
traces of Cataclysms and Change visible on the earth's surface； followed
by two books； one a mathematical book； the other on political geography；
and completed by a mapwhich one would like to see： but not a trace
of all remains； save a few quoted fragments …
We are such stuff As dreams are made of。
But if Eratosthenes had hold of eternal fact and law on one point；
there was a contemporary who had hold of it in more than one。 I mean
Archimedes； of whom； as I have said； we must speak as of an Alexandrian。
It was as a mechanician； rather than as an astronomer； that he gained his
reputation。 The stories of his Hydraulic Screw； the Great Ship which he
built for Hiero； and launched by means of machinery； his crane； his war…
engines； above all his somewhat mythical arrangement of mirrors； by
which he set fire to ships in the harbourall these； like the story of his
detecting the alloy in Hiero's crown； while he himself was in the bath； and
running home undressed shouting ＇Greek text： eureeka＇all these are
schoolboys' tales。 To the thoughtful person it is the method of the man
which constitutes his real greatness； that power of insight by which he
solved the two great problems of the nature of the lever and of hydrostatic
pressure； which form the basis of all static and hydrostatic science to this
day。 And yet on that very question of the lever the great mind of
Aristotle babblesneither sees the thing itself； nor the way towards seeing
it。 But since Archimedes spoke； the thing seems self…evident to every
schoolboy。 There is something to me very solemn in such a fact as this。
It brings us down to some of the very deepest questions of metaphysic。
This mental insight of which we boast so much； what is it？ Is it
altogether a process of our own brain and will？ If it be； why have so few
the power； even among men of power； and they so seldom？ If brain
alone were what was wanted； what could not Aristotle have discovered？
Or is it that no man c