seconds, the orbit we have to
scrutinise is only as large as the apparent size of a penny-piece at the
distance of one mile. It would require very careful measurement to make
out the form of a penny a mile off, even with good telescopes. If the
penny were tilted a little, it would appear, not circular, but oval; and
it would be possible, by measuring this oval, to determine how much the
penny was tilted. All this requires skilful work: the errors, viewed
intrinsically, may not be great, but viewed with reference to the whole
size of the quantities under consideration, they are very appreciable.
We therefore find the errors of observation far more prominent in
observations of this class than is generally the case when the
mathematician assumes the task of discussing the labours of the
observer.

The interpretation of Herschel's discovery was not accomplished by
himself; the light of mathematics was turned on his observations of the
binary stars by Savary, and afterwards by other mathematicians. Under
their searching enquiries the errors of the measurements were disclosed,
and the observations were purified from the grosser part of their
inaccuracy. Mathematicians could then apply to their corrected materials
the methods of enquiry with which they were familiar; they could deduce
with fair precision the actual shape of the orbit of the binary stars,
and the position of the plane in which that orbit is contained. The
result is not a little remarkable. It has been proved that the motion of
each of the stars is performed in an ellipse which contains the centre
of gravity of the two stars in its focus. This has been actually shown
to be true in many binary stars; it is believed to be true in all. But
why is this so important? Is not motion in an ellipse common enough?
Does not the earth revolve in an ellipse round the sun? And do not the
planets also revolve in ellipses?

It is this very fact that elliptic motion is so common in the planets of
the solar system which renders its discovery in binary stars of such
importance. From what does the elliptic motion in the solar system
arise? Is it not due to the law of attraction, discovered by Newton,
which states that every mass attracts every other mass with a force
which varies inversely as the square of the distance? That law of
attraction had been found to pervade the whole solar system, and it
explained the movements of the bodies of our system with marvellous
fidelity. But