ratio of the inverse
square, it appeared that gravity would, at the moon's orbit, draw a body
through more than fifteen feet." In view of this discrepancy he gave up
the inquiry for sixteen years, until in 1682, having obtained better
data, he successfully renewed it. "He had been mistaken in the magnitude
of the earth, and consequently in the distance of the moon, which is
determined by measurements of which the earth's radius is the base." It
was not, therefore, a mistake as to the law or as to the nature of the
forces concerned (namely, the law of the inverse square and the identity
of celestial with terrestrial gravity), but as to the circumstances in
which the agents (earth and moon) were combined, that prevented his
calculations being verified. (_Hist. Ind. Sc._: VII. ii. 3.)

(3) One or more of the agents affecting the result may have been
overlooked and omitted from the estimate. Thus, an attempt to explain
the tides by taking account only of the earth and the moon, will not
entirely agree with the facts, since the sun also influences the tides.
This illustration, however, shows that when the conclusion of a
deductive explanation does not entirely agree with the facts, it is not
always to be inferred that the reasoning is, properly speaking, wrong;
it may be right as far as it goes, and merely inadequate. Hence (a) in
such cases an opportunity occurs of applying the Method of Residues, by
discovering the agent that must be allowed for in order to complete the
explanation. And (b) the investigation of a phenomenon is often
designedly begun upon an imperfect basis for the sake of simplicity; the
result being regarded as a first approximation, to be afterwards
corrected by including, one by one, the remaining agents or
circumstances affecting the phenomenon, until the theory is complete;
that is, until its agreement with the facts is satisfactory.

(4) We may have included among the data of our reasonings agents or
circumstances that do not exist or do not affect the phenomenon in
question. In the early days of science purely fanciful powers were much
relied upon: such as the solid spheres that carried the planets and
stars; the influence of the planets upon human destiny; the tendency of
everything to seek "its own place," so that fire rises to heaven, and
solids fall to the earth; the "plastic virtue" of the soil, which was
once thought to have produced fossils. When, however, such conceptions
hindered the prog