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 stadia—31,500 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 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 map—which 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 harbour—all 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 εὕρηκα—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 babbles—neither 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 can see a thing unless God shows it him?  Is it that in each separate act of induction, that mysterious and transcendental process which cannot, let logicians try as they will, be expressed by any merely logical formula, Aristotelian or other—is it I say, that in each separate act of induction we do not find the law, but the law is shown to us, by Him who made the law? Bacon thought so.  Of that you may find clear proof in his writings.  May not Bacon be right?  May it not be true that God does in science, as well as in ethics, hide things from the wise and prudent, from the proud, complete, self-contained systematiser like Aristotle, who must needs explain all things in heaven and earth by his own formulæ, and his entelechies and energies, and the rest of the notions which he has made for himself out of his own brain, and then pack each thing away in its proper niche in his great cloud-universe of conceptions?  Is it that God hides things from such men many a time, and reveals them to babes, to gentle, affectionate, simple-hearted men, such as we know Archimedes to have been, who do not try to give an explanation for a fact, but feel how awful and divine it is, and wrestle reverently and stedfastly with it, as Jacob with the Angel, and will not let it go, until it bless them?  Sure I am, from what I have seen of scientific men, that there is an intimate connection between the health of the moral faculties and the health of the inductive ones; and that the proud, self-conceited, and passionate man will see nothing: perhaps because nothing will be shown him.

But we must leave Archimedes for a man not perhaps so well known, but to whom we owe as much as to the great Syracusan—Hipparchus the astronomer.  To his case much which I have just said applies.  In him astronomic science seemed to awaken suddenly to a true inductive method, and after him to fall into its old slumber for 300 years.  In the meantime Timocharis, Aristyllus, and Conon had each added their mites to the discoveries of Eratosthenes: but to Hipparchus we owe that theory of the heavens, commonly called the Ptolemaic system, which, starting from the assumption that the earth was the centre of the universe, attempted to explain the motions of the heavenly bodies by a complex system of supposed eccentrics and epicycles.  This has of course now vanished before modern discoveries.  But its value as a scientific attempt lies in this: that the method being a correct one, correct results were obtained, though starting from a false assumption; and Hipparchus and his successors were enabled by it to calculate and predict the changes of the heavens, in spite of their clumsy instruments, with almost as much accuracy as we do now.

For the purpose of working out this theory he required a science of trigonometry, plane and spherical: and this he accordingly seems to have invented.  To him also we owe the discovery of that vast gradual change in the position of the fixed stars, in fact, of the whole celestial system, now known by the name of the precession of the equinoxes; the first great catalogue of fixed stars, to the number of 1080; attempts to ascertain whether the length of years and days were constant; with which, with his characteristic love of truth, he seems to have been hardly satisfied.  He too invented the planisphere, or mode of representing the starry heavens upon a plane, and is the father of true geography, having formed the happy notion of mapping out the earth, as well as the heavens, by degrees of latitude and longitude.

Strange it is, and somewhat sad, that we should know nothing of this great man, should be hardly able to distinguish him from others of the same name, but through the works of a commentator, who wrote and observed in Alexandria 300 years after, during the age of the Antonines.  I mean, of course, the famous Ptolemy, whose name so long bore the honour of that system which really belonged to Hipparchus.

This single fact speaks volumes for the real weakness of the great artificial school of literature and science founded by the kings of Egypt.  From the father of Astronomy, as Delambre calls him, to Ptolemy, the first man who seems really to have appreciated him, we have not a discovery, hardly an observation or a name, to fill the gap.  Physical sages there were; but they were geometers and mathematicians, rather than astronomic observers and inquirers.  And in spite of all the huge appliances and advantages of that great Museum, its inhabitants were content, in physical science, as in all other branches of thought, to comment, to expound, to do everything but open their eyes and observe facts, and learn from them, as the predecessors whom they pretended to honour had done.  But so it is always.  A genius, an original man appears.  He puts himself boldly in contact with facts, asks them what they mean, and writes down their answer for the world’s use.  And then his disciples must needs form a school, and a system; and fancy that they do honour to their master by refusing to follow in his steps; by making his book a fixed dogmatic canon; attaching to it