to Prop.  III. (a) (ch. xv.  Sec. 7).  Still, it is supposable that, in the second instance, D or E may be the cause of the increment of p; and that, in the third instance, F or G may be its cause:  though the probability of such vicarious causation decreases rapidly with the increase of instances in which A and p vary together.  And, since an actual investigation of this type must rely on observation, it is further possible that some undiscovered cause, X, is the real determinant of both A and p and of their concomitant variations.

Professor Ferri, in his Criminal Sociology, observes:  “I have shown that in France there is a manifest correspondence of increase and decrease between the number of homicides, assaults and malicious wounding, and the more or less abundant vintage, especially in the years of extraordinary variations, whether of failure of the vintage (1853-5, 1859, 1867, 1873, 1878-80), attended by a remarkable diminution of crime (assaults and wounding), or of abundant vintages (1850, 1856-8, 1862-3, 1865, 1868, 1874-5), attended by an increase of crime” (p. 117, Eng. trans.).  And earlier he had remarked that such crimes also “in their oscillations from month to month display a characteristic increase during the vintage periods, from June to December, notwithstanding the constant diminution of other offences” (p. 77).  This is necessarily an appeal to the canon of Concomitant Variations, because France is never without her annual vintage, nor yet without her annual statistics of crime.  Still, it is an argument whose cogency is only that of Agreement, showing that probably the abuse of the vintage is a cause of crimes of violence, but leaving open the supposition, that some other circumstance or circumstances, arising or varying from year to year, may determine the increase or decrease of crime; or that there is some unconsidered agent which affects both the vintage and crimes of violence.  French sunshine, it might be urged, whilst it matures the generous grape, also excites a morbid fermentation in the human mind.

Difference in Variations may be symbolically represented thus (no other change having concurred): 

     A B A’ B A’’ B
    p q, p’ q, p’’ q.

Here the accompanying phenomena are always the same B/q; and the only point in which the successive instances differ is in the increments of A (A’, A’’) followed by corresponding increments of p (p’, p’’):  hence the increment of A is the cause of the increment of p.

For examples of the application of this method, the reader should refer to some work of exact science.  He will find in Deschanel’s Natural Philosophy, c. 32, an account of some experiments by which the connection between heat and mechanical work has been established.  It is there shown that “whenever work is performed by the agency of heat” [as in driving an engine], “an amount of heat disappears