(1) We may not have accurately ascertained the laws, or the modes of operation, or the amounts of the forces present.  Thus, the rate at which bodies fall was formerly believed to vary in proportion to their relative weights; and any estimate based upon this belief cannot agree with the facts.  Again, the corpuscular theory of light, namely, that the physical cause of light is a stream of fine particles projected in straight lines from the luminous object, though it seemed adequate to the explanation of many optical phenomena, could not be made to agree with the facts of interference and double refraction.

(2) The circumstances in which the agents are combined may not have been correctly conceived.  When Newton began to inquire whether the attraction of the earth determined the orbit of the moon, he was at first disappointed.  “According to Newton’s calculations, made at this time,” says Whewell, “the moon, by her motion in her orbit, was deflected from the tangent every minute through a space of thirteen feet.  But by noticing the space which bodies would fall in one minute at the earth’s surface, and supposing this to be diminished in the 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.