never meet. To the end they would still be just one yard apart.

But suppose that, as you fixed them in the ground, you gave them a careless little tilt each towards the other. Would they then go on always apart?

No. Sooner or later they must touch. How soon would depend on how much you had made them slant at the first. They might meet in two or three yards; or in a hundred yards; or in half-a-mile. From the length of your base-line-exactly one yard-and from the angle at each end of it, one who understood the right method might reckon roughly about how far off that meeting-spot would be.

The Moon is much farther away than any tower or hill on Earth. There is all the difference between possibly one or two hundred miles, and over two hundred thousand miles.

To discover the Moon's distance from any ordinary base-line was found impossible. So a new plan came up. Two stations, widely apart, were chosen. Astronomers at these two places made each their observations of the Moon's exact position in the sky, and compared notes.

That plan proved a success. The Moon's parallax at last could be measured, and calculations made. Time after time, with ever better instruments, it was undertaken, till now we know accurately how far away from us she floats.

But the same scheme with the Sun was a failure. From a position ninety-three millions of miles away it would not work. Not even a base-line eight thousand miles long was enough to cause any "shift" of position on his part. Other plans had to be tried; and the first

66

to meet with real success was by means of the transit of Venus." The passing of that small planet across the brilliant face of the Sun gave a chance which was eagerly seized, when once it was known to be a possibility.

Here, again, observers were planted in two places, as widely apart as the size of our Earth permitted, having between them a base-line nearly eight thousand miles long. Each had to note with extremest care, first, the instant when that tiny dark body was just within the Sun's outer edge-"limb" is the correct wordand also the exact instant when it just quitted the further edge. And here at last was found the shift of position, not shown in the position of the Sun himself, but in the tiny difference of time noted by the two observers, so widely parted, in the moment of Venus passing between Earth and Sun.

You understand, of course, that on these rare occasions-only twice in a century-Venus is no nearer than usual to the Sun. She merely passes exactly between Sun and Earth, so as to be seen against him. And from the minute difference in time of these apparent" touchings," as seen from opposite ends of the base-line, the Sun's distance could be reckoned.

III. BUT THE STARS?

Then came the question of star-distances. If the Sun lay nearly one hundred millions of miles away, how far off might be the fixed stars?

For this great problem the diameter of our Earth proved useless. It had been tried and tried in vain. It was

66

far too short a base-line. Not a star stirred in response. Not the faintest sign of a parallax" could be seen. And no possibilities existed here of any other heavenly body crossing the face of a star; for no star in all the sky has a “face” for us, except our Sun. Each to our sight is a point only, with no breadth, no disc.

A grand idea came up. If the diameter of Earth was as nothing in respect of star-distances, what of our yearly journey round the Sun? What of Earth's two positions in mid-summer and mid-winter? Would not that give a base-line long enough to make even the stars show a shift" in their positions? Twice ninety-three millions of miles! A tremendous base-line, this.

66

And it was tried. Close and careful observations were taken at one date of several stars; and six months later, when the Earth was about one hundred and eighty millions of miles away from where she had been at the date of the first observations, these were repeated.

Failure again! Not a star seemed to stir. Not a single shift, however minute, could be detected. Not one hoped-for parallax was found. Even that enormous base-line sank, it appeared, to but one point in relation to the stars.

It was desperately disappointing. But astronomers would not despair. Again and again they tried this plan--for indeed no other was known-with more and more delicate instruments. And at last they were rewarded. At last one star here, another there, did show a very, very minute shifting of its position; a very, very tiny seeming displacement, due to Earth's huge change of place.

From these slight results the distances of a few stars

could be roughly calculated. Not, of course, with anything like exactness, but enough to be real and dependable.

Only a few, among the thousands and millions seen. With by far the greater number no stir becomes visible. Many more have been measured since that date, yet the great majority of them lie beyond our reach.

Still it is something to know, even roughly, how far, how very, very far away, even the nearer ones lie; how vast is the dividing chasm which separates us from the tens of millions-probably the hundreds of millions-of blazing suns of which our wonderful Universe is composed.

You may perhaps say that I have not really explained the manner in which such calculations are worked out. No; for that I fear you must go in for mathematics and for trained teachers, who will carry you through such preliminary instructions as are necessary before you can enter into the whole question. All that I have attempted to do, is to give you a slight foundation-idea of the gist of the matter, to make you see how it has been approached. If you have vision enough to gain a glimmer of what these calculations really mean, you will at least see something of the wonder-not only of the actual knowledge gained, but also of the minds of those men who, in the first instance, grappled with such stupendous difficulties, and overcame them. The results, won by their tireless courage and perseverance, may be mastered by those who have had no technical training; and in this little book my aim has been to give, simply and clearly, many such results.

It may be of interest, if I add, with regard to this question of base-lines and triangles and "shifts," that you yourself are perpetually acting after the same mode.

When you judge of the distance of anything that you see as you do, mechanically, and for the greater part unconsciously—you are using a base-line and triangles. The space between your two eyes is your base-line and the object at which you look, whether near or far, is seen by each eye in a slightly different position—against a slightly different background-from that in which it is seen by the other. Your two eyes combine the two views, and your brain at lightning speed works out the problem and gives you the result.

If you had only one eye you would not have that base-line. But you could carry out the same plan by first looking with your one eye, and then moving your head, so as to take a second view with the same eye, much as when astronomers observed the stars from one position in Earth's yearly pathway round the Sun, and six months later observed them again from another. The principle in both cases is the same.

In thus judging by sight, we are by no means always successful. Much depends on natural aptitude, much also on practice. Look at an aeroplane passing overhead, and make a guess at its height above the ground. You are all but certain to give an estimate very wide of the mark.

But those who are constantly in practice may arrive at an extraordinary accuracy of judgment. I have just come across the following statement, with regard to British anti-aircraft gunners in the war: “Archie