tury. It is well known that
we shall at least come very near the truth when we say that the
planets revolve around the sun, and the satellites around their
primaries according to the law of gravitation. We may regard all
these bodies as projected into space, and thus moving according to
laws similar to that which governs the motion of a stone thrown
from the hand. If two bodies alone were concerned, say the sun
and a planet, the orbit of the lesser around the greater would be
an ellipse, which would never change its form, size, or position.
That the orbits of the planets and asteroids do change, and that they
are not exact ellipses, is due to their attraction upon each other.
The question is, do these mutual attractions completely explain all
the motions down to the last degree of refinement? Does any world
move otherwise than as it is attracted by other worlds?

Two different lines of research must be brought to bear on the
question thus presented. We must first know by the most exact and
refined observations that the astronomer can make exactly how a
heavenly body does move. Its position, or, as we cannot directly
measure distance, its direction from us, must be determined as
precisely as possible from time to time. Its course has been
mapped out for it in advance by tables which are published in the
"Astronomical Ephemeris," and we may express its position by its
deviation from these tables. Then comes in the mathematical problem
how it ought to move under the attraction of all other heavenly bodies
that can influence its motion. The results must then be compared,
in order to see to what conclusion we may be led.

This mathematical side of the question is of a complexity beyond
the powers of ordinary conception. I well remember that when,
familiar only with equations of algebra, I first looked into a
book on mechanics, I was struck by the complexity of the formulae.
But this was nothing to what one finds when he looks into a work on
celestial mechanics, where a single formula may fill a whole chapter.
The great difficulty arises from the fact that the constant action
upon a planet exerted at every moment of time through days and
years by another planet affects its motion in all subsequent time.
The action of Jupiter upon our earth this morning changes its motion
forever, just as a touch upon a ball thrown by a pitcher will change
the direction of the ball through its whole flight.

The wondrous perfecti