ses, there could be no rational thinking; and yet by this
indispensable tendency, men are perpetually led to found, on limited
experience, propositions which they wrongly assume to be universal or
absolute. In one sense, however, this can scarcely be regarded as an
evil; for without premature generalizations the true generalization
would never be arrived at. If we waited till all the facts were
accumulated before trying to formulate them, the vast unorganized mass
would be unmanageable. Only by provisional grouping can they be brought
into such order as to be dealt with; and this provisional grouping is
but another name for premature generalization. How uniformly men follow
this course, and how needful the errors are as steps to truth, is well
illustrated in the history of Astronomy. The heavenly bodies move round
the Earth in circles, said the earliest observers: led partly by the
appearances, and partly by their experiences of central motions in
terrestrial objects, with which, as all circular, they classed the
celestial motions from lack of any alternative conception. Without this
provisional belief, wrong as it was, there could not have been that
comparison of positions which showed that the motions are not
representable by circles; and which led to the hypothesis of epicycles
and eccentrics. Only by the aid of this hypothesis, equally untrue, but
capable of accounting more nearly for the appearances, and so of
inducing more accurate observations--only thus did it become possible
for Copernicus to show that the heliocentric theory is more feasible
than the geocentric theory; or for Kepler to show that the planets move
round the sun in ellipses. Yet again, without the aid of Kepler's more
advanced theory of the Solar system, Newton could not have established
that general law from which it follows, that the motion of a heavenly
body is not necessarily in an ellipse, but may be in any conic section.
And lastly, it was only after the law of gravitation had been verified,
that it became possible to determine the actual courses of planets,
satellites, and comets; and to prove that, in consequence of
perturbations, their orbits always deviate, more or less, from regular
curves. In these successive theories we may trace both the tendency men
have to leap from scanty data to wide generalizations, that are either
untrue or but partially true; and the necessity there is for such
transitional generalizations as steps to the final