214 
crease in population can be represented by the curve given 
in Fig. IV. If the figures for the apprehensions for drunken- 
ness in these towns be grouped by twenties as before, and 
a curve be run nearly through the points representing the 
means, Fig. V. is obtained, in which the curve, though not 
so regular as those of figures 3 and 4, still takes in general 
the opposite slant to the curve of Fig. IV. 
This method of examining the numbers is unsatisfactory 
in this point, that a town such as Liverpool, with 490,000 
inhabitants, has only the same effect on the course 
of the curve as Southport with 20,000 inhabitants. 
Fig. VI. represents tlie proportion of public-houses 
per ten thousand of the population on this principle. 
The population of each town is taken as the nearest ten 
thousand, to save trouble in calculating. The towns are 
then grouped together in hundred thousands, so that each 
square now represents, instead of a town, a population of 
100,000. The numbers at the top refer to the towns with 
the same numbers in Fig. I. included in each 100,000. If 
the numbers of apprehensions for drunkenness for 10,000 of 
the population in each of these populations of 100,000 be 
grouped by tens as before, the curve in Fig. VII. is obtained. 
This does not now follow the opposite course to the public- 
house curve so regularly as did those of Figs. 3 and 4, though 
it is still, on the whole, higher on the right hand where the 
public-house curve is lower. 
The two great rises are caused chiefly : the first by Man- 
chester and Salford; the second by Liverpool, as will be seen 
by referring to the numbers in Fig. VII. oj)posite the rises. 
If the towns be arranged in order of apprehensions for 
drunkenness for the year 1875, from Cambridge with one 
in 500 to Liverpool with one in 20, it at once becomes 
evident, that on the whole, in the north of England, there 
is a greater proportion of apprehensions than in the south. 
The following are the towns arranged in that order ; — 
