“Father,” exclaimed James one day, “the captain has been giving me
a riddle which I cannot guess. He asks where a pound of shot is not a
pound. Is he joking with me?
Not at all, lad. A bag of shot weighing a pound in London, or even in
Melbourne, will not weigh a pound on the equator.
What queer things you do tell me! How can that be?
You know that the world attracts you.
Yes; I know when I jump up I am soon brought down, and sometimes
unpleasantly so, too.
As the world is round, and everywhere the world pulls things down to
its surface, it is as if it were drawing all to the centre. This is
called the _Attraction of Gravitation_.
And I suppose that like as fire is hotter the nearer you get to it, so
does the attraction get greater the nearer you get to the centre of the
earth.
True; but can you guess how this gravitation can be weight?
I know when I pull a thing, it is as if I pushed it, or put a weight on
it. So the pulling of the earth will make the thing attracted feel as
if a weight were on it.
And can you not see why a pound should somewhere not be a pound?
No; unless I made a big hole towards the centre, and then the pound
weight would be heavier. But you told me the world was round, and it
must be as far from the centre at London and Melbourne, as at the
equator.
But if from trial it be found that the pound really is less at the
Line, what would it prove?
It proves what I can’t see, that the earth at the equator is farther
off the centre than what it is at London or Melbourne, and that would
make the earth not a true Globe.
Neither is it my son: though the difference is but little. It is about
a dozen miles thicker down to the centre at the Line than at the poles.
Then, as London and Melbourne are each nearly half-way between the line
and the pole they will be nearer by six miles to the centre than the
equator is.
You have solved the problem, and understand that the world is not a
sphere, but what is called an Oblate Spheroid, being flattened at the
poles.
As I cannot easily find out by weighing that a pound is not a pound:
can you tell me any other way of proving that the earth is not quite
round, dear father?
Yes, I can. Do you see the reason why the pendulum returns down when it
is moved up?
The gravitation, to be sure.
If a thing weighs heavier in one place than another through a
difference of gravitation will there be a difference in the two places
with the pendulum?
I should fancy that where the earth pulled the harder the pendulum
would come down the quicker.
If it came down quicker it would rise quicker; that is, the beat would
be quicker. What effect would this have upon the clock?
The faster it beat, the faster the wheels would be moved, and the
faster the hands would turn on the face.
Just so: the clock would be faster in time when the pendulum beat
quicker, and slower in time when the pendulum beat slower.
But how could I find this out, father?
This way. It is ascertained that in London a pendulum must be 39-1/7
inches from the top to the middle of the swinging-bob to beat a true
second at a time.
Then I am sure the London pendulum will not be pulled down so hard at
the equator, and so it will be longer coming and going.
What must I do, then, to make my London pendulum beat seconds on the
equator?
Why, shorten it a little bit.
Yes; or, what is the same thing, move up the weight at the end of the
pendulum a little. I must shorten it one-tenth of an inch, or else it
will lose sixteen hours in the year.
Then all the clocks carried to Melbourne from London will be wrong.
Will they go too fast or too slowly in Victoria?
They will be a little too slow, as Melbourne is nearer the equator than
London is.
If a Melbourne clock-maker want his second pendulum to beat seconds in
London what directions must he give?
He must tell the folks in London to lengthen the pendulum a bit.
You will see that by the world being flattened at the poles the degrees
of latitude will differ. One close to the equator measures 68-3/4
miles, in Victoria about 69 miles, in England 69-1/8, while in Lapland
it would be 69-1/4.
What would be the mean length of a degree?
About 69-1/20 miles.
Let me multiply that by 360, to find the mean circumference of the
world; I have it--24,858 miles.”