s it to
trace out an ellipse instead of a straight line.

The great problem to be solved is now easily stated. There must be some
external agent constantly influencing the earth. What is that agent,
whence does it proceed, and to what laws is it submitted? Nor is the
question confined to the earth. Mercury and Venus, Mars, Jupiter, and
Saturn, unmistakably show that, as they are not moving in rectilinear
paths, they must be exposed to some force. What is this force which
guides the planets in their paths? Before the time of Newton this
question might have been asked in vain. It was the splendid genius of
Newton which supplied the answer, and thus revolutionised the whole of
modern science.

The data from which the question is to be answered must be obtained from
observation. We have here no problem which can be solved by mere
mathematical meditation. Mathematics is no doubt a useful, indeed, an
indispensable, instrument in the enquiry; but we must not attribute to
mathematics a potency which it does not possess. In a case of this kind,
all that mathematics can do is to interpret the results obtained by
observation. The data from which Newton proceeded were the observed
phenomena in the movement of the earth and the other planets. Those
facts had found a succinct expression by the aid of Kepler's laws. It
was, accordingly, the laws of Kepler which Newton took as the basis of
his labours, and it was for the interpretation of Kepler's laws that
Newton invoked the aid of that celebrated mathematical reasoning which
he created.

The question is then to be approached in this way: A planet being
subject to _some_ external influence, we have to determine what that
influence is, from our knowledge that the path of each planet is an
ellipse, and that each planet sweeps round the sun over equal areas in
equal times. The influence on each planet is what a mathematician would
call a force, and a force must have a line of direction. The most simple
conception of a force is that of a pull communicated along a rope, and
the direction of the rope is in this case the direction of the force.
Let us imagine that the force exerted on each planet is imparted by an
invisible rope. Kepler's laws will inform us with regard to the
direction of this rope and the intensity of the strain transmitted
through it.

The mathematical analysis of Kepler's laws would be beyond the scope of
this volume. We must, therefore, confine ourselves to the res