SOCIAL AND ECONOMIC THEORY 
19 
great as the price change, i. e. that a 1 per cent. fluctua- 
tion in price was accompanied by a 3 per cent. fluctuation 
in profit. But in the case of a unit variation in output, 
the change in profit was only quite a small fraction over 
unity. In these investigations all the coefficients of cor- 
relation were very high, and it may be said that I was 
merely putting into elaborate figures conclusions that 
would be obvious to ordinary reflection. But the real 
object was to find the ratio of variation and especially to 
disentangle the effects of price changesand outputchanges. 
The fact that demand for coal tends to be very inelastic 
in the neighbourhood of any normal condition is also de- 
ducible from the inquiry. I also showed that increase in 
the prosperity of the coal industry may be symptomatic 
of increased trade generally, if due to increased output 
only. The correlation between railway profits and the 
price of coal was negative, but high and significant, i. e. if 
the price of coal was markedly increased, then the railway 
profits were clearly less in the following year—a lag of 
a year giving the most marked correlation. The deviation 
of railway profits from the trend was about one-quarter 
of the opposite deviation of coal prices. Gas profits had a 
similar negative correlation with coal prices, and the de- 
viation about two-thirds in amplitude. The monthly 
correlation of the buying price of raw textiles in an Eastern 
market, and the selling price in London, over seven years, 
proved to be almost complete (0-97), so that fluctuations 
in a merchant’s total profits were entirely due to volume 
of trade. Cotton spinning gave an interesting result. 
‘ There is very little regular relationship between the 
profits of cotton spinning and either the purchase price 
of raw cotton or the sale price of yarn, but the changes 
in the difference between the two prices is more indica- 
tive of changes in the amount of profits. Of late years 
the quantity of raw cotton imported has been some 
criterion of the prosperity of the trade. The purchase 
price of raw cotton and the sale price of yarn are very 
closely related indeed.