B C
q r

as an instance of the absence of p obtained deductively from the whole phenomenon

A B C
p q r

by our knowledge of the laws of B and C; so that

A B C
p q r

is an instance of the presence of p, differing otherwise from

B C
q r

in nothing except that A is also present.  By the Canon of Difference, therefore A is the cause of p.  Or, again, when phenomena thus treated are strictly quantitative, the method may be based on Prop.  III. (b), ch. xv.  Sec. 7.

Of course, if A can be obtained apart from B C and directly experimented with so as to produce p, so much the better; and this may often be done; but the special value of the method of Residues appears, when some complex phenomenon has been for the most part accounted for by known causes, whilst there remains some excess, or shortcoming, or deviation from the result which those causes alone would lead us to expect, and this residuary fact has to be explained in relation to the whole.  Here the negative instance is constituted by deduction, showing what would happen but for the interference of some unknown cause which is to be investigated; and this prominence of the deductive process has led some writers to class the method as deductive.  But we have seen that all the Canons involve deduction; and, considering how much in every experiment is assumed as already known (what circumstances are ‘material,’ and when conditions may be called ’the same’), the wonder is that no one has insisted upon regarding every method as concerned with residues.  In fact, as scientific explanation progresses, the phenomena that may be considered as residuary become more numerous and the importance of this method increases.

Examples:  The recorded dates of ancient eclipses having been found to differ from those assigned by calculation, it appears that the average length of a day has in the meanwhile increased.  This is a residuary phenomenon not accounted for by the causes formerly recognised as determining the rotation of the earth on its axis; and it may be explained by the consideration that the friction of the tides reduces the rate of the earth’s rotation, and thereby lengthens the day.  Astronomy abounds in examples of the method of Residues, of which the discovery of Neptune is the most famous.

Capillarity seems to be a striking exception to the principle that water (or any liquid) ‘finds its level,’ that being the condition of equilibrium; yet capillarity proves to be only a refined case of equilibrium when account is taken of the forces of adhesion exerted by different kinds of bodies in contact.

“Many of the new elements of Chemistry,” says Herschel, “have been detected in the investigation of residual phenomena.”  Thus, Lord Rayleigh and Sir W. Ramsay found that nitrogen from the atmosphere was slightly heavier than nitrogen got from chemical sources; and, seeking the cause of this difference, discovered argon.