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 o