deflecting force. Newton constructed such a diagram, and, measuring the
amount of the moon's departure from a tangential rectilinear course in
one minute, determined this to be, by his calculation, thirteen feet.
Obviously, then, the force acting upon the moon is one that would cause
that body to fall towards the earth to the distance of thirteen feet
in the first minute of its fall. Would such be the force of gravitation
acting at the distance of the moon if the power of gravitation varies
inversely as the square of the distance? That was the tangible form in
which the problem presented itself to Newton. The mathematical solution
of the problem was simple enough. It is based on a comparison of the
moon's distance with the length of the earth's radius. On making this
calculation, Newton found that the pull of gravitation--if that were
really the force that controls the moon--gives that body a fall of
slightly over fifteen feet in the first minute, instead of thirteen
feet. Here was surely a suggestive approximation, yet, on the other
band, the discrepancy seemed to be too great to warrant him in the
supposition that he had found the true solution. He therefore dismissed
the matter from his mind for the time being, nor did he return to it
definitely for some years.

{illustration caption = DIAGRAM TO ILLUSTRATE NEWTON'S LAW OF
GRAVITATION (E represents the earth and A the moon. Were the earth's
pull on the moon to cease, the moon's inertia would cause it to take the
tangential course, AB. On the other hand, were the moon's motion to be
stopped for an instant, the moon would fall directly towards the
earth, along the line AD. The moon's actual orbit, resulting from these
component forces, is AC. Let AC represent the actual flight of the moon
in one minute. Then BC, which is obviously equal to AD, represents the
distance which the moon virtually falls towards the earth in one minute.
Actual computation, based on measurements of the moon's orbit, showed
this distance to be about fifteen feet. Another computation showed that
this is the distance that the moon would fall towards the earth under
the influence of gravity, on the supposition that the force of gravity
decreases inversely with the square of the distance; the basis of
comparison being furnished by falling bodies at the surface of the
earth. Theory and observations thus coinciding, Newton was justified in
declaring that the force that pulls the moon towards the eart