If, on the other hand, we omit the clause “[no other change having concurred,]” the Canon is a statement of the method of Agreement as applicable to the increment of a phenomenon instead of to the phenomenon as a whole; and it is then subject to the imperfections of that method:  that is to say, it leaves open the possibilities, that an inquirer may overlook a plurality of causes; or may mistake a connection of two phenomena, which (like the flash and report of a gun) are co-effects of a common cause, for a direct relation of cause and effect.

It may occur to the reader that we ought also to distinguish Qualitative and Quantitative Variations as two orders of phenomena to which the present method is applicable.  But, in fact, Qualitative Variations may be adequately dealt with by the foregoing methods of Agreement, Double Agreement, and Difference; because a change of quality or property entirely gets rid of the former phase of that quality, or substitutes one for another; as when the ptarmigan changes from brown to white in winter, or as when a stag grows and sheds its antlers with the course of the seasons.  The peculiar use of the method of Variations, however, is to formulate the conditions of proof in respect of those causes or effects which cannot be entirely got rid of, but can be obtained only in greater or less amount; and such phenomena are or course, quantitative.

Even when there are two parallel series of phenomena the one quantitative and the other qualitative—­like the rate of air-vibration and the pitch of sound, or the rate of ether-vibration and the colour-series of the spectrum—­the method of Variations is not applicable.  For (1) two such series cannot be said to vary together, since the qualitative variations are heterogeneous:  512:  576 is a definite ratio; but the corresponding notes, C, D, in the treble clef, present only a difference.  Hence (2) the correspondence of each note with each number is a distinct fact.  Each octave even is a distinct fact; there is a difference between C 64 and C 128 that could never have been anticipated without the appropriate experience.  There is, therefore, no such law of these parallel series as there is for temperature and change of volume (say) in mercury.  Similar remarks apply to the physical and sensitive light-series.

We may illustrate the two cases of the method thus (putting a dash against any letter, A’ or p’, to signify an increase or decrease of the phenomenon the letter stands for):  Agreement in Variations (other changes being admissible)—­

A B C           A’ D E            A’’ F G
p q r         p’ s t          p’’ u v

Here the accompanying phenomena (B C q r, D E s t, F G u v) change from time to time, and the one thing in which the instances agree throughout is that any increase of A (A’ or A’’) is followed or accompanied by an increase of p (p’ or p’’):  whence it is argued that A is the cause of p, according