If we now suppose the interior of the shell to be filled up solid,
that will make no difference, because the mass of the part B D C will
only be increased vastly thereby, while the mass of A B C will remain
the same; the two parts only increasing their proportion to each
other, and thus coming to be for the earth--in the Harton Colliery
experiments--what we represented them to be at page 24; and we can now
proceed to find the attractive force of each of the two masses for the
bob of the pendulum which is as the inverse square of their distances
from it. These distances may be taken, without any very great stretch
of conscience, as one-tenth of a mile and 3999·75 miles; because the
centre of gravity of the segment A B C will be about that distance from
O, and that of B D C cannot be adequately represented by a greater
sum than 3999·75, always supposing the diameter of the earth to be
8000 miles. Thus the squares of these two distances will be 0·01 and
15,898,000 miles respectively, and the relative force of attraction
for the pendulum of the two segments A B C and B D C will be as 1 ×
0·01 and 772,846,315, and 772,846,315 × 15,898,000; that is as 1 is
to 1,228,671,000,000,000,000. Here then we get confirmed the unbelief
in the theory we expressed at pages 23 and 24. Surely no one will be
bold enough to assert that by decreasing the total attractive force
of the earth by a little less than a 1-1/4 trillionth part cut off
from one side of it, the want of homogeneity in what remains will not
only not decrease its attractive force at the centre, but increase it
so as to make a pendulum be lessened by 1/38,400th part of its time
in beating one second. This fraction of time is quite small enough to
inspire doubt of any theory founded upon it; and if there ever is a
quantity in mathematics that can be called negligible, the fraction of
attractive force found above ought to be included in the same category.
We may therefore assert that no human measurements could find a true
difference between the beats of a seconds pendulum at the top and
bottom of the pit at the Harton Colliery. If all the people who have
puzzled themselves with this theory had spent an hour or two in making
the above calculations before they began them, there would have been
no experiments made, and the theory would have died almost ere it was
born. Those who believed in it may have looked upon a particle as a
negligible quantity, but as the whole earth is made up of particles a
little thought would have put an end to such a notion. What puzzles
us is how such a theory could be formed by people who knew nothing
whatever of the nature of the interior of the earth at a depth of even
one mile, and how they could speculate on its want of homogeneity
without knowing anything of how the density of 5·66 is made up in it?
To suppose that the earth is made up of strata of different densities,
and that each is in some degree elliptical--the ellipticity of one
Public-domain text, read in full here on John Shaqi.
Reviews
Reviews
No reviews yet
Be the first to share your thoughts on this work.
Join the Discussion
Join the discussion
Sign in to leave a comment or review.
Sign InorCreate an account