THE DISTANCES OF THE STARS.

I must now tell you something about the distances of the stars. I

shall not make the attempt to explain fully how astronomers make such

measurements, but I will give you some notion of how it is done. You

may remember I showed you how we found the distance of a globe that

was hung from the ceiling. The principle of the method for finding the

distance of a star is somewhat similar, except that we make the two

observations not from the two ends of a table, not even from opposite

sides of the earth, but from two opposite points on the earth’s orbit,

which are therefore at a distance of 186,000,000 miles. Imagine that on

Midsummer Day, when standing on the earth here, I measure with a piece

of card the angle between the star and the sun. Six months later, on

Midwinter Day, when the earth is at the opposite point of its orbit,

I again measure the angle between the same star and the sun, and we

can now determine the star’s distance by making a triangle. I draw a

line a foot long, and we will take this foot to represent 186,000,000

miles, the distance between the two stations; then placing the cards

at the corners, I rule the two sides and complete the triangle, and the

star must be at the remaining corner; then I measure the sides of the

triangle, and find how many feet they contain, and recollecting that

each foot corresponds to 186,000,000 miles, we discover the distance of

the star. If the stars were comparatively near us, the process would be

a very simple one; but, unfortunately, the stars are so extremely far

off that this triangle, even with a base of only one foot, must have

its sides many miles long. Indeed, astronomers will tell you that there

is no more delicate or troublesome work in the whole of their science

than that of discovering the distance of a star.

In all such measurements we take the distance from the earth to the

sun as a conveniently long measuring-rod, whereby to express the

results. The nearest stars are still hundreds of thousands of times

as far off as the sun. Let us ponder for a little on the vastness of

these distances. We shall first express them in miles. Taking the sun’s

distance to be 93,000,000 miles, then the distance of the nearest fixed

star is about twenty millions of millions of miles--that is to say,

we express this by putting down a 2 first, and then writing thirteen

ciphers after it. It is, no doubt, easy to speak of such figures, but

it is a very different matter when we endeavor to imagine the awful

magnitude which such a number indicates. I must try to give some

illustrations which will enable you to form a notion of it. At first I

was going to ask you to try and count this number, but when I found it

would require at least 300,000 years, counting day and night without

stopping, before the task was over, it became necessary to adopt some

other method.

When on a visit in Lancashire I was once kindly permitted to visit a

cotton mill, and I learned that the cotton yarn there produced in a

single day would be long enough to wind round this earth twenty-seven

times at the equator. It appears that the total production of cotton

yarn each day in all the mills together would be on the average about

155,000,000 miles. In fact, if they would only spin about one-fifth

more, we could assert that Great Britain produced enough cotton yarn

every day to stretch from the earth to the sun and back again! It is

not hard to find from these figures how long it would take for all the

mills in Lancashire to produce a piece of yarn long enough to reach

from our earth to the nearest of the stars. If the spinners worked

as hard as ever they could for a year, and if all the pieces were

then tied together, they would extend to only a small fraction of the

distance; nor if they worked for ten years, or for twenty years, would

the task be fully accomplished. Indeed, upwards of 400 years would be

necessary before enough cotton could be grown in America and spun in

this country to stretch over a distance so enormous. All the spinning

that has ever yet been done in the world has not formed a long enough

thread!

There is another way in which we can form some notion of the immensity

of these sidereal distances. You will recollect that, when we were

speaking of Jupiter’s moons (p. 219), I told you of the beautiful

discovery which their eclipses enabled astronomers to make. It was

thus found that light travels at the enormous speed of about 185,000

miles per second. It moves so quickly that within a single second a ray

would flash two hundred times from London to Edinburgh and back again.

We said that a meteor travels one hundred times as swiftly as a

rifle-bullet; but even this great speed seems almost nothing when

compared with the speed of light, which is 10,000 times as great.

Suppose some brilliant outbreak of light were to take place in a

distant star--an outbreak which would be of such intensity that the

flash from it would extend far and wide throughout the universe.

The light would start forth on its voyage with terrific speed. Any

neighboring star which was at a distance of less than 185,000 miles

would, of course, see the flash within a second after it had been

produced. More distant bodies would receive the intimation after

intervals of time proportional to their distances. Thus, if a body

were 1,000,000 miles away the light would reach it in from five to six

seconds, while over a distance as great as that which separates the

earth from the sun the news would be carried in about eight minutes. We

can calculate how long a time must elapse ere the light shall travel

over a distance so great as that between the star and our earth. You

will find that from the nearest of the stars the time required for the

journey will be over three years. Ponder on all that this involves.

That outbreak in the star might be great enough to be visible here,

but we could never become aware of it till three years after it had

happened. When we are looking at such a star to-night we do not see it

as it is at present, for the light that is at this moment entering

our eyes has travelled so far that it has been three years on the way.

Therefore, when we look at the star now we see it as it was three years

previously. In fact, if the star were to go out altogether, we might

still continue to see it twinkling for a period of three years longer,

because a certain amount of light was on its way to us at the moment

of extinction, and so long as that light keeps arriving here, so long

shall we see the star showing as brightly as ever. When, therefore, you

look at the thousands of stars in the sky to-night, there is not one

that you see as it is now, but as it was years ago.

I have been speaking of the stars that are nearest to us, but there

are others much farther off. It is true we cannot find the distance

of these more remote objects with any degree of accuracy, but we

can convince ourselves how great that distance is by the following

reasoning. Look at one of the brightest stars. Try to conceive that the

object was carried away further into the depths of space, until it was

ten times as far from us as it is at present, it would still remain

bright enough to be recognized in quite a small telescope; even if it

were taken to one hundred times its original distance it would not have

withdrawn from the view of a good telescope; while if it retreated

one thousand times as far as it was at first it would still be a

recognizable point in our mightiest instruments. Among the stars which

we can see with our telescopes, we feel confident there must be many

from which the light has expended hundreds of years, or even thousands

of years, on the journey. When, therefore, we look at such objects, we

see them, not as they are now, but as they were ages ago; in fact, a

star might have ceased to exist for thousands of years, and still be

seen by us every night as a twinkling point in our great telescopes.

Remembering these facts, you will, I think, look at the heavens with a

new interest. There is a bright star, Vega or Alpha Lyræ, a beautiful

gem, so far off that the light from it which now reaches our eyes

started before many of my audience were born. Suppose that there are

astronomers residing on worlds amid the stars, and that they have

sufficiently powerful telescopes to view this globe, what do you think

they would observe? They will not see our earth as it is at present,

they will see it as it was years, and sometimes many years, ago. There

are stars from which, if England could now be seen, the whole of the

country would be observed at this present moment to be in a great

state of excitement at a very auspicious event. Distant astronomers

might notice a great procession in London, and they could watch the

coronation of a youthful queen amid the enthusiasm of a nation. There

are other stars still further, from which, if the inhabitants had good

enough telescopes, they would now see a mighty battle in progress not

far from Brussels. One splendid army could be beheld hurling itself

time after time against the immovable ranks of the other. They would

not, indeed, be able to hear the ever-memorable, “Up, Guards, and at

them!” but there can be no doubt that there are stars so far away that

the rays of light which started from the earth on the day of the

battle of Waterloo are only just arriving there. Further off still,

there are stars from which a bird’s-eye view could be taken at this

very moment of the signing of Magna Charta. There are even stars from

which England, if it could be seen at all, would now appear, not as the

great England we know, but as a country covered by dense forests, and

inhabited by painted savages, who waged incessant war with wild beasts

that roamed through the island. The geological problems that now puzzle

us would be quickly solved could we only go far enough into space and

had we only powerful enough telescopes. We should then be able to view

our earth through the successive epochs of past geological time; we

should be actually able to see those great animals whose fossil remains

are treasured in our museums tramping about over the earth’s surface,

splashing across its swamps, or swimming with broad flippers through

its oceans. Indeed, if we could view our own earth reflected from

mirrors in the stars, we might still see Moses crossing the Red Sea, or

Adam and Eve being expelled from Eden.

So important is the subject of star distance that I am tempted to give

one more illustration in order to bring before you some conception of

how vast such distances are. I shall take, as before, the nearest of

the stars so far as known to us, and I hope to be forgiven for taking

an illustration of a practical and a commercial kind instead of one

more purely scientific. I shall suppose that a railway is about to

be made from London to Alpha Centauri. The length of that railway,

of course, we have already stated: it is twenty billions of miles.

So I am now going to ask your attention to the simple question as to

the fare which it would be reasonable to charge for the journey. We

shall choose a very cheap scale on which to compute the price of a

ticket. The parliamentary rate here is, I believe, a penny for every

mile. We will make our interstellar railway fares much less even than

this; we shall arrange to travel at the rate of one hundred miles for

every penny. That, surely, is moderate enough. If the charges were so

low that the journey from London to Edinburgh only cost fourpence,

then even the most unreasonable passenger would be surely contented.

On these terms how much do you think the fare from London to this

star ought to be? I know of one way in which to make our answer

intelligible. There is a National Debt with which your fathers are,

unhappily, only too well acquainted; you will know quite enough about

it yourselves in those days when you have to pay income tax. This debt

is so vast that the interest upon it is about sixty thousand pounds

a day, the whole amount of the National Debt being six hundred and

thirty-eight millions of pounds (April, 1898).

If you went to the booking office with the whole of this mighty sum

in your pocket--but stop a moment; could you carry it in your pocket?

Certainly not, if it were in sovereigns. You would find that after you

had as many sovereigns as you could conveniently carry there would

still be some left--so many, indeed, that it would be necessary to get

a cart to help you on with the rest. When the cart had as great a load

of sovereigns as the horse could draw there would be still some more,

and you would have to get another cart; but ten carts, twenty carts,

fifty carts, would not be enough. You would want five thousand of these

before you would be able to move off towards the station with your

money. When you did get there and asked for a ticket at the rate of one

hundred miles for a penny, do you think you would get any change? No

doubt some little time would be required to count the money, but when

it was counted the clerk would tell you that there was not enough, that

he must have nearly two hundred millions of pounds more.

That will give some notion of the distance of the nearest star, and we

may multiply it by ten, by one hundred, and even by one thousand, and

still not attain to the distance of some of the more remote stars that

the telescope shows us.

On account of the immense distances of the stars we can only perceive

them to be mere points of light. We can never see a star to be a globe

with marks on it like the moon, or like one of the planets--in fact,

the better the telescope the smaller does the star seem, though,

of course, its brightness is increased with every addition to the

light-grasping power of the instrument.