force, the ham attracts the earth exactly as much
as the earth does the ham. So what the butcher really does is to find
how much or how strongly the ham attracts the earth, and he calls that
pull the weight of the ham. On the same principle, the astronomer finds
the weight of a body by finding how strong is its attractive pull on
some other body. If the butcher, with his spring-balance and a ham,
could fly to all the planets, one after the other, weigh the ham on
each, and come back to report the results to an astronomer, the latter
could immediately compute the weight of each planet of known diameter,
as compared with that of the earth. In applying this principle to the
heavenly bodies, we at once meet a difficulty that looks
insurmountable. You cannot get up to the heavenly bodies to do your
weighing; how then will you measure their pull? I must begin the answer
to this question by explaining a nice point in exact science.
Astronomers distinguish between the weight of a body and its mass. The
weight of objects is not the same all over the world; a thing which
weighs thirty pounds in New York would weigh an ounce more than thirty
pounds in a spring-balance in Greenland, and nearly an ounce less at
the equator. This is because the earth is not a perfect sphere, but a
little flattened. Thus weight varies with the place. If a ham weighing
thirty pounds were taken up to the moon and weighed there, the pull
would only be five pounds, because the moon is so much smaller and
lighter than the earth. There would be another weight of the ham for
the planet Mars, and yet another on the sun, where it would weigh some
eight hundred pounds. Hence the astronomer does not speak of the weight
of a planet, because that would depend on the place where it was
weighed; but he speaks of the mass of the planet, which means how much
planet there is, no matter where you might weigh it.

At the same time, we might, without any inexactness, agree that the
mass of a heavenly body should be fixed by the weight it would have in
New York. As we could not even imagine a planet at New York, because it
may be larger than the earth itself, what we are to imagine is this:
Suppose the planet could be divided into a million million million
equal parts, and one of these parts brought to New York and weighed. We
could easily find its weight in pounds or tons. Then multiply this
weight by a million million million, and we shall have a weight of the
planet. Th