James had a long talk with the captain one day about the telescope,
and got a capital lesson about the magnifying power being according
to the character and size of the glasses used. The sailors called the
instrument the “Bring ’em near;” and it does make distant objects
look as if near. It was explained to the boy that the stars were of
different magnitudes or sizes, first, second, third, &c., according to
their relative distances. The following conversation followed between
the father and son:--
“Now, my boy, I must try and give you some idea of the penetrating
power of light, that you may get an idea of the enormous distances of
the stars. You are aware that the more distant they are the less their
light. A star of the first or nearest magnitude will have one hundred
times the light of one of the sixth magnitude. A telescope, therefore,
gathering one hundred times the ordinary light, will make the sixth
look as near as the first.
And will it be one hundred times further off?
No; light increases or diminishes according to the square of the
distance.
I know. If the light be one hundred times less, the star will be
ten times further off, for the square of ten is one hundred. I can
understand now that a thing is only seen by the help of light. I do not
see many stars, because their light is too little for my eyes to take
in. The telescope has bigger eyes to take in the light of the distant
stars and nebulæ.
The pupil of the eye is but one-eighth of an inch in diameter. An
object glass of twelve inches diameter is, therefore, ninety-six, or
say one-hundred times as long. As the light seen is according to the
square of the diameter, the telescope of twelve inches will receive one
hundred times one hundred, or ten thousand times more light.
But is there a way of measuring the quantity of light?
There is. We find that the sun has twenty-two thousand millions of
times more light than the nearest of the fixed stars.
Then, the square root of this ought to tell how much further off it is.
Let me see. It will be about 150,000.
Yes. If the sun were put back 150,000 times further than it is, it
ought to look as brightly as that star. If it does not, it is because
it is really smaller than the star.
What! 150,000 times 95 millions!
But that is nothing; for it is only to the first rank. What of the
twentieth magnitude?
Yes. But you say the nebulæ are further off than that.
I may tell you that if the sun moved three times as fast as the world
does, in its six hundred millions of miles a year, it would take two
hundred and fifty millions of years to get to as far as Lord Rosse’s
telescope could see.
That takes my breath away.
Hear a little more. Light comes from the sun to us in eight minutes. It
will take sixty thousand years to come from one of those stars Lord de
Rosse saw. In fact his telescope has enlarged our universe one hundred
and twenty-five million times.
Then I think religious people ought to thank astronomers for showing
them more of the greatness of God. Those who only thought of him as the
Creator of the three thousand stars, to be seen by the naked eye, could
not have such a notion of his vast power as those who know of millions
upon millions of suns.”
* * * * *
After this, James was left to digest such wonderful lessons. When his
first astonishment had passed away, his curiosity was excited to know
more about the distances of the stars, so that he might form a simpler
idea of the thing. He took, therefore, another occasion of bringing up
the subject in these words:--
“Father, do you really believe the stars are so far off?
I am obliged to believe many things I do not understand, upon the
testimony of trustworthy witnesses; but in this case I can form a
good guess of the truth. Do you remember what I once told you of the
parallax, or angle of observation of the sun or moon?
Yes. That of the moon was 57 minutes, and the sun 8-3/4 seconds. A
degree is 60 minutes, and a minute 60 seconds.
Very well. Then 57 minutes, or 3420 seconds, will be four hundred times
as much as the other. If the moon be 240,000 miles off, the sun will be
four hundred times further or 96,000,000.
But how do you get this parallax?
Distances are calculated by the angle made in looking at an object from
two places. The two lines of sight cross one another. A great base is
needed to view a distant object, or else no angle can be observed.
Astronomers take the diameter of the earth’s orbit.
That is twice ninety-five millions of miles.
With that base--that is, looking at a star from both sides of our
orbit, or at six months’ interval--we could get the two lines crossing
one another, and so making an angle. The further the object, the more
minute the angle. Only a few of the fixed stars could be observed in
this way, as they generally are too far off to give an angle.
I know an equilateral triangle has its three angles equal to two right
angles; and with ninety degrees for one right angle, each angle of the
triangle will have sixty degrees. But I suppose no star parallax could
be one degree.
No; nor a minute, the sixtieth part of one degree. When the object
makes an angle of a second, or sixtieth of a minute, from a base line
of one hundred and ninety millions of miles, the distance of the star
will be about twenty millions of millions of miles.
Is there any star making the second angle?
The _alpha_ of the Centaur is about that, and is one of the nearest of
fixed stars.
That the nearest to us, and yet so far! Do tell me the distance of some
others.
There is one, 61 Cygni, of the Swan, with one-third of a second; and,
therefore, three times the distance of the _alpha_ Centaur. There is
a star in the Lyre which is one-fifth of a second. Grand Arcturus is
one-eight. The North Polar Star is one-tenth. Pretty Capella, of the
Kid, is one-twentieth; that is, twenty times farther back than _a_
Centaur. As it looks one of the brightest stars, it must be very large.
What of old Sirius?
The angle he makes with our orbit diameter is one-fourth of a second;
so that he is about 80,000,000,000,000 miles.
Thank you, dear father, for these terrible long figures.
Their great distance may give us a good guess of their great size.
I know the size of the sun to be half-a-degree in the heavens, at a
distance of ninety-five millions of miles, and yet it is really eight
hundred and eighty-six thousand miles diameter, I have been told. When,
then, a star is millions of millions of miles away, I am sure it must
be a big one to be seen at all.
It is so. If the sun were thrust back as far as the star _a_ Centaur,
it is calculated that it would not shine with more than one-third of
the light that star now gives us; it must, therefore, be not more than
one-third its size.
But you said Sirius was four times farther off than the Centaur, father.
Yes; and it gives four times as much light. It is, then, probably four
times as large. It must be, therefore, many times larger than the sun.
I am sure it ought to have more planets turning round it than the sun
has, or else have them much larger in size.”