Beatrice M. Cave and Karl Pearson 
353 
insignificant. Railways (— "204 + '240), Shipping (+ '232 + "237), International 
Commerce (+ -142 + -245), Post (- -183 + -246), Stamp Duties (+-222 + 238), 
Savings (+ -046 + -250) and Coal (+ -152 + ■245). Apart therefore from the 
general increase of consumption with the time, during which time the general 
prosperity of the nation has increased, it would not appear that the consumption 
of a luxury has any organic relationship to prosperity. We do not find tliat a 
favourable trade fluctuation is associated with increased consumption of luxuries. 
In fact the suggestion arises that in the case of tobacco the consumption ma}' be 
greater in a period of depression. 
Conclusions. While we lay no special stress on any of the results suggested 
by the difference correlations above studied — far more intimate economic know- 
ledge of Italian affairs and methods of measurement would be requisite — we yet 
venture to insist on one or two general considerations. 
The very superficial statements, so frequently met with, that such and such 
variates, both changing rapidly with the time, are essentially causative will 
doubtless cease to have any scientific currency, directly the method of variate 
differences is fully appreciated. We shall no longer assert that the fall of 
the phthisis death-rate can be off-hand causatively associated with the con- 
temporaneous rise in the number of persons dying in institutions, or that the 
increased expenditure on luxuries is necessarily a measure of increased national 
prosperity. 
If we turn as in the present paper to the actual correlatiijns of the indices 
themselves, we find in every case an arid and scarcely undulating waste of high 
correlation. No one can obtain any nourishment whatever from the statement 
that the Tobacco Index is correlated with the Revenue Index to the amount of "983 
and with the Savings Bank Index to the extent of "984 ! The organic relationship 
between these variates is wholly obscured by the continuous increase of all three of 
them with the time. But when we proceed to sixth differences and see that the 
consumption of tobacco has little, if any, relation to revenue, and is associated 
substantially but negatively with savings, we seem to touch realities, and realities 
of some worth. Again what can we learn, if we are told that Shipping Index is 
correlated to the extent of "99 with both the Revenue and the Savings Bank Indices? 
We might imagine, that increase of shipping was not only the primary cause of 
increase in Italian revenue, but also the essential origin of any increase in the Italian 
peasant's and artisan's savings ! An appeal to the variate difference method shows 
how fallacious such imaginings would be ! An examination of the sixth difference 
correlations shows that while prosperity of the revenue is closely associated with 
trade as measured by shipping ("77), the correlation is not nearly perfect; on 
the other hand there appears to be no significant organic correlation at all 
(—•154 + '244) between the prosperity of the revenue and the savings of the 
Italian populace. As we have noted a knowledge of local conditions and methods 
