angles, without approaching the object at all. You see then how we can get a good long line of sixty or seventy miles. Now, as the earth is a sphere or nearly so, if you travel due north a 360th part of the earth's circumference, you will find that the pole star has assumed a position one degree higher in the heavens. Accordingly, if you can measure distances and angles, the determination of the circumference of the earth is reduced to a matter of mere multiplication. The old Indians had got thus far; the old Greeks too. Two hundred and thirty years before the Christian era, Eratosthenes, the librarian of the Alexandrian library, observed the meridian height of the sun at Alexandria, at the time of the summer solstice, and then set to work to measure the distance up the Nile to Syene, where the granite quarries still show the marks of the chisel that cut out those wonderful obelisks from them. Here he found, or somebody found for him, a telescope ready to his hand-the earliest telescope on record. It was a reflecting telescope, like Herschel's, polished by nature's own machinery. The mirror was the surface of standing water, and the tube was one of those vertical shafts which, as in Joseph's well, have stood the wear of ages, and are wonderful even in the land of the pyramids and the sphinxes. Far, far down in the bowels of the earth, the brighter stars were visible by day. This telescope disclosed the fact, that Syene is just under the northern tropic. And so Eratosthenes, like his great benefactor Alexander, conquered the world. He did not weep because there were no more worlds to conquer; for were not the bright orbs, the allies of his first victory, like the Thebans, sure to become an easy prey to his chariot-wheels? But the work of Eratosthenes was done, and they gave him as a reward a mountain in the moon, which bears his name.

To be sure, the 250,000 stadia which Eratosthenes estimated as the circumference of the earth, wàs a rough enough approximation as compared with the precision of modern times. But it was

the nations of Europe have set themselves to the task. One instance deserves mention.

In 1791-2, the National Convention of France conceived the magnificent idea of establishing a new standard for everything-morals, money, and measure. "Let the heavens," they said, “furnish

new units of time, and the earth new

"units of space. Let the week, and "the month, and the year yield up their "ancient prerogatives. Let the former "history of the world be forgotten, and "let all history date from this time. "Let the month be divided into thirty days, and let the sabbath occur every "tenth day. Let the day be divided "into ten hours, and let new dials be "constructed to show them. Let a "girdle be drawn round the earth, which "shall connect Paris with the poles: "let this girdle be the standard of 'measure, and let men be sent out to "ascertain its amount." A magnificent order, truly! Yet it does seem easy enough to count by thirties and by tens -to make the month thirty days, and the week ten; but to measure the circumference of the earth, this is a work, a labour! It so happened, however, that the thirty days, and the new sundials, and the unscriptural sabbaths failed to struggle into existence-a higher power protected France from herself; whilst the measure of the meridians-a work beset with appalling difficulties was accomplished; and the mètre, the ten-millionth part of the measured quadrant of the earth's circumference, is the national standard throughout France to this day.

One

The work was carried on when France was embroiled with all Europe. The great men who executed it had to combat with national prejudices and popular superstitions in a foreign land. Privation, anxiety, and fatigue laid some of the foremost of them low. owed his life to the protection afforded by a Spanish prison; another broke his heart, on regaining his liberty, by the discovery that the observations he had made from his prison windows would

angles, without approaching the object at all. You see then how we can get a good long line of sixty or seventy miles. Now, as the earth is a sphere or nearly so, if you travel due north a 360th part of the earth's circumference, you will find that the pole star has assumed a position one degree higher in the heavens. Accordingly, if you can measure distances and angles, the determination of the circumference of the earth is reduced to a matter of mere multiplication. The old Indians had got thus far; the old Greeks too. Two hundred and thirty years before the Christian era, Eratosthenes, the librarian of the Alexandrian library, observed the meridian height of the sun at Alexandria, at the time of the summer solstice, and then set to work to measure the distance up the Nile to Syene, where the granite quarries still show the marks of the chisel that cut out those wonderful obelisks from them. Here he found, or somebody found for him, a telescope ready to his hand-the earliest telescope on record. It was a reflecting telescope, like Herschel's, polished by nature's own machinery. The mirror was the surface of standing water, and the tube was one of those vertical shafts which, as in Joseph's well, have stood the wear of ages, and are wonderful even in the land of the pyramids and the sphinxes. Far, far down in the bowels of the earth, the brighter stars were visible by day. This telescope disclosed the fact, that Syene is just under the northern tropic. And so Eratosthenes, like his great benefactor Alexander, conquered the world. He did not weep because there were no more worlds to conquer; for were not the bright orbs, the allies of his first victory, like the Thebans, sure to become an easy prey to his chariot-wheels? But the work of Eratosthenes was done, and they gave him as a reward a mountain in the moon, which bears his name.

To be sure, the 250,000 stadia which Eratosthenes estimated as the circumference of the earth, wàs a rough enough approximation as compared with the precision of modern times. But it was

the nations of Europe have set themselves to the task. One instance deserves mention.

In 1791-2, the National Convention of France conceived the magnificent idea of establishing a new standard for everything morals, money, and measure. "Let the heavens," they said, "furnish "new units of time, and the earth new "units of space. Let the week, and "the month, and the year yield up their "ancient prerogatives. Let the former "history of the world be forgotten, and "let all history date from this time. "Let the month be divided into thirty

66

days, and let the sabbath occur every "tenth day. Let the day be divided "into ten hours, and let new dials be "constructed to show them. Let a "girdle be drawn round the earth, which "shall connect Paris with the poles: "let this girdle be the standard of

measure, and let men be sent out to "ascertain its amount." A magnificent order, truly! Yet it does seem easy enough to count by thirties and by tens -to make the month thirty days, and the week ten; but to measure the circumference of the earth, this is a work, a labour! It so happened, however, that the thirty days, and the new sundials, and the unscriptural sabbaths failed to struggle into existence-a higher power protected France from herself; whilst the measure of the meridians-a work beset with appalling difficulties was accomplished; and the mètre, the ten-millionth part of the measured 'quadrant of the earth's circumference, is the national standard throughout France to this day.

The work was carried on when France was embroiled with all Europe. The great men who executed it had to combat with national prejudices and popular superstitions in a foreign land. Privation, anxiety, and fatigue laid some of the foremost of them low. One owed his life to the protection afforded by a Spanish prison; another broke his heart, on regaining his liberty, by the discovery that the observations he had made from his prison windows would

From

M. Arago, in his autobiography, gives an amusing, but perhaps an exaggerated, sketch of his own share in these labours. He tells us that he commenced by pacing to and fro, for the space of six months, on the narrow platform of a rock which overlooks the Mediterranean, to watch for the signal-light from the island of Iviza. From this airy spot he was transferred to the closer atmosphere of the castle of Belver, wounded, and a prisoner. Here he had the satisfaction of reading in the Spanish papers a detailed account of his own execution. Judging that the announcement was but the prelude to the event, he looked about for the means of escape. the window of his prison he finds he can leap into the sea, and he resolves on doing so; conceiving, as he says, "that it is as well to be drowned as to be hanged." But he is not drowned. He reaches a ship, and is conveyed to the coast of Africa, where he finds the Moors almost as uncivilized as the Spaniards. So he is not sorry when he is allowed to return to his work. Once more in Spain, he is not long in discovering that brigandage is one of the institutions of the country. His temporary station, on the top of a mountain near Culléra, is visited, one stormy night, by the chief bandit of the district. The astronomer makes him his friend, and the work proceeds merrily under his protection.

Enough. We have measured the earth, but we are a great way from the stars still. Our yard measure has brought us thousands of miles on our journey; but the stars are millions of millions of miles away, and how are we to get at them? We shall see. Remember, then, that, when we had a base line of a few miles, we could determine the distance of an object seen from either end, by means of angles alone. In the same way, we get at the distance of the sun, or of a planet, by the longer base-line of the earth itself. We get at it roughly, it must be confessed. Copernicus, Tycho, even Kepler himself, had no idea that the sun is so far from us as he really is. Had the sun been fixed im

movably in the heavens, it might have been easy, or, at least, it might have been deemed easy, to compare his

distance with the size of the earth. But the sun wanders among the stars and rolls round the earth, and thus seems to defy the efforts of the measurer. It was the good fortune of James Gregory to point out a method by which his distance may be determined, spite of his unsteadiness. The orbits of the two planets, Mercury and Venus, lie between the sun and the earth, so that those planets occasionally cross the face of the sun-Mercury frequently, Venus more rarely. It occurred to Gregory that observers at different parts of the earth's surface would witness a transit across different parts of the sun-one seeing it cross the centre, another observing it graze the edge. And, as the time it took in crossing might be readily ascertained in either case, the places at which it crossed would be thereby determined. And thus, knowing the positions of the two places of observation, and the corresponding positions of the projection of the planet on the sun's disk, the determination of the distance of the sun would, by a little help from theory, be reduced to a mere matter of triangles. Perhaps Gregory hardly appreciated the full value of the suggestion he was making. At any rate, nothing followed the publication of his hint for a great number of years. At length, about the beginning of the last century, it assumed, in the mind of Halley, the definite and practicable form which renders it now the corner-stone of astronomy. Halley perceived that the planet Venus was greatly to be preferred to Mercury for the determination of the sun's distance from the earth. His lucid statements and earnest exhortations aroused the whole astronomical world, and a transit of Venus was anxiously awaited. Halley himself, indeed, when he directed attention to the importance of the method, had no hope of living to see it tested. He stood like Moses on the top of Pisgah, and looked on the Promised Land; but to cross the Jordan was not his earthly lot. He had been laid with

angles, without approaching the object at all. You see then how we can get a good long line of sixty or seventy miles. Now, as the earth is a sphere or nearly so, if you travel due north a 360th part of the earth's circumference, you will find that the pole star has assumed a position one degree higher in the heavens. Accordingly, if you can measure distances and angles, the determination of the circumference of the earth is reduced to a matter of mere multiplication. The old Indians had got thus far; the old Greeks too. Two hundred and thirty years before the Christian era, Eratosthenes, the librarian of the Alexandrian library, observed the meridian height of the sun at Alexandria, at the time of the summer solstice, and then set to work to measure the distance up the Nile to Syene, where the granite quarries still show the marks of the chisel that cut out those wonderful obelisks from them. Here he found, or somebody found for him, a telescope ready to his hand-the earliest telescope on record. It was a reflecting telescope, like Herschel's, polished by nature's own machinery. The mirror was the surface of standing water, and the tube was one of those vertical shafts which, as in Joseph's well, have stood the wear of ages, and are wonderful even in the land of the pyramids and the sphinxes. Far, far down in the bowels of the earth, the brighter stars were visible by day. This telescope disclosed the fact, that Syene is just under the northern tropic. And so Eratosthenes, like his great benefactor Alexander, conquered the world. He did not weep because there were no more worlds to conquer; for were not the bright orbs, the allies of his first victory, like the Thebans, sure to become an easy prey to his chariot-wheels? But the work of Eratosthenes was done, and they gave him as a reward a mountain in the moon, which bears his name.

To be sure, the 250,000 stadia which Eratosthenes estimated as the circumference of the earth, wàs a rough enough approximation as compared with the precision of modern times. But it was

the nations of Europe have set themselves to the task. One instance deserves mention.

In 1791-2, the National Convention of France conceived the magnificent idea of establishing a new standard for everything morals, money, and measure. "Let the heavens," they said, "furnish "new units of time, and the earth new "units of space. Let the week, and "the month, and the year yield up their "ancient prerogatives. Let the former "history of the world be forgotten, and "let all history date from this time. "Let the month be divided into thirty "days, and let the sabbath occur every "tenth day. Let the day be divided "into ten hours, and let new dials be "constructed to show them. Let a

'girdle be drawn round the earth, which "shall connect Paris with the poles: "let this girdle be the standard of measure, and let men be sent out to "ascertain its amount." A magnificent order, truly! Yet it does seem easy enough to count by thirties and by tens -to make the month thirty days, and the week ten; but to measure the circumference of the earth, this is a work, a labour! It so happened, however, that the thirty days, and the new sundials, and the unscriptural sabbaths failed to struggle into existence-a higher power protected France from herself; whilst the measure of the meridians—a work beset with appalling difficulties was accomplished; and the mètre, the ten-millionth part of the measured 'quadrant of the earth's circumference, is the national standard throughout France to this day.

The work was carried on when France was embroiled with all Europe. The great men who executed it had to combat with national prejudices and popular superstitions in a foreign land. Privation, anxiety, and fatigue laid some of the foremost of them low. One owed his life to the protection afforded by a Spanish prison; another broke his heart, on regaining his liberty, by the discovery that the observations he had made from his prison windows would