Beatrice M. Cave and Karl Pearson 
351 
differences persistent in sign. Even the correlation with Tobacco is small, falling 
and insignificant (< -115 ± -247), and that with Coal which might be supposed to 
be high as marking good trade times is hardly significant although apparently 
rising (? > "270 ± •232). Lastly the correlation of Revenue with International 
Commerce is again small, falling, and insignificant (< -214 ± -239). Thus Revenue 
or the "entrato effectivo dello state" seems to provide an index which has little 
valuable relation to any other characteristic of prosperity beyond shipping. 
(e) International Commerce. Here we find no single final individual index 
correlation greater than -54, which is that for Shipping. The next most important 
correlations are with Post (>-47) and Stamp Duty (c. -46). With Railways the 
correlation is zero, and with Revenue also falling and insignificant. With Savings, 
Coal, Tobacco and Coffee the correlations are all insignificant; in fact in the last 
three cases not only are the values less than their probable errors, but they are 
still falling. It is thus clear that in Italy the total of Exports and Imports is 
no measure of all-round prosperity, they do not immediately increase either 
savings or the consumption of luxuries. 
(/) Post and Telegrams. Here we have the lowest series of correlations we 
have yet reached. Post values have no significant relation to fluctuations in 
Railway (c. - -20 + -24), to Shipping (- -059 ± -249), Stamp Duties (- '027 + ^oO), 
Coal (- -050 ± •250), Tobacco (+ '108 + -247) or Coffee (- -133 + -240) Indices. It 
is significantly correlated only with International Commerce (> + '47i'19) and, 
perhaps, significantly with Savings (+ "336 + "222) but negatively with Revenue 
(c. — -38 + "21). In short the number of letters and telegrams in Italy is hardly a 
mark of any other favourable fluctuation in prosperity, beyond International 
Commerce. 
(g) Stamp Duties. This Index is correlated positively and significantly with 
International Commerce (c. + '46 + "20) and positively, and doubtfully with Savings 
(c. + '35 + '22). It is correlated insignificantly and negatively with Railways 
(-•261 ±-2-iS), Shipping (--009 ± -250), Revenue (--250 ±-234), Post (--027 ±-250), 
and Tobacco (— "129 + "246) ; it is correlated positively and insignificantly with 
Coal (+ -052 ± -250) and Coffee (+ "222 ± "238). Thus again freed from continuous 
time changes, fluctuations in the Stamp Duty Index are of small value as a 
measure of contemporaneous general prosperity. 
(/<) Savings Bank Index. There are practically only two correlations of any 
importance with Savings and these are both negative, namely those with Railways 
(- -431 + -204) and with Tobacco (- -431 ± -204). Hence it would appear that 
when the Italian peoj^le is in a saving mood, it spares on transit by rail and on 
the consumption of tobacco, and when it expends on these luxuries, then it does 
not save. Savings have small and possibly not significant cori'elations with Post 
(> + "33 ± "22) and Stamp Duties (<-l-"353 + "219), and insignificant and positive 
correlations with International Commerce (> + ^27 + "23), Coal (> + '19 + ^24) 
