350 Illustrations of the Variate Difference Correlation Method 
to zero, now stands at something greater than '42 and might rise higher, but 
the relation to International Commerce as a whole is zero, which suggests that 
the goods imported and exported are not in the bulk carried by rail. Further 
although the final value of the Railway and Post correlation is scarcely sensible 
(— "214 + "239), it has been continuously negative from the second difference, and 
thus suggests that increased expenditure on the post means lessened profit for 
the railways. This might be interpreted in two ways : (i) that business con- 
ducted by post or telegram lessens rail intercommunication b}^ person, or (ii) that 
in the case of state-railways, there is not an increased profit to the railways from 
carrying larger mails. Bat still more remarkable are the negative correlations of 
Stamp Duties, Savings, Tobacco and Coffee with Railways ; none of them are very 
large, and all but savings, perhaps, of the order of their probable errors. But 
taken as a whole they suggest that when the Italian spends little money in going 
about, then he saves more, or spends more on such luxuries as tobacco and coffee. 
Lastl}^ we have the Coal Index. It might be supposed that a year with great 
coal importation would signify great railway activity, and this is the judgment 
which would be made from the raw correlations of these variates. But the actual 
facts are exhibited in a correlation still falling at the sixth difference and hardly 
significant having regard to its probable error. The inferences formed must be : 
(i) that imported coal is used largely at the ports of disembarcation or travels 
inland by other than railway transit, (ii) that the imported coal is largely used on 
the railways themselves and that its cost is a heavy tax on their resources. 
(c) Shipping Index. As we might anticipate this is highly correlated with 
(i) Railivays (c. "62), (ii) Revenue (c. "75) and less highly but very significantly with 
(iii) International Commerce (c. 54) and (iv) Coal (c. "58), but it appears to have 
no relation whatever with Post, Stamp-Duties and Savings, and when we come to 
luxuries, their importation is clearly not a factor of shipping prosperity. Neither 
in the case of Tobacco nor of Coffee are the correlations really significant ; with 
the former we have an increasing negative correlation and with the latter a 
decreasing positive one already below its probable error. Thus we see that 
neither directly by bulk of importation nor indirectly by immediate increase of 
consumption, does a rise of shipping mark significant rises in the use of luxuries 
such as Tobacco and Coffee. It would be of interest to ascertain whether in- 
creased consumption of luxuries does not raXhev follow than accompany favourable 
trade fluctuations. 
{d) Revenue Index. This index as we might expect is fairly highly cor- 
related with Shipping (c. "75). It has relatively small relation to Railways 
(•422 + "206) at least at the sixth difference and a somewhat similar value 
(c. '42 + -20) for Coffee. Thus the suggestions arise that revenue is but little 
produced by the railways and that coffee is not a very large factor of the custom 
dues. It is astonishing to find, however, that Post, Stamps and Savings have 
negative correlations with Revenue of — "388 + '213, — "255 + "234 and — '154 + '244 
respectively, which, if scarcely significant, have been in each case for several 
