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Mr. Chamberlain has exhibited the proportion by means 
of a curve in black ink which I have copied in Fig. I. The 
numbers are taken from the Blue Book Police (Counties 
and Boroughs) Reports for the year ending September, 1875. 
In this figure the towus of Table I. are supposed to be 
arranged in order from left to right, and the height of the 
curve opposite each town represents the number of persons 
to each public-house. Owing to want of space, only every 
fifth town is actually printed. Mr. Chamberlain then puts a 
mark opposite each town on the same diagram showing the 
number of persons proceeded against for drunkenness in 
proportion to the population in that town during the same 
year, the numbers varying from one in 500 in Cambridge 
and Maidstone, to one in 20 in Tynemouth, South Shields, 
and Liverpool. The marks thus placed are joined by a red 
ink curve. Mr. Chamberlain remarks that “if the paradox 
of the supporters of free trade in drink were sustainable by 
these statistics the red line would incline throughout from 
right to left in the opposite direction to the black line ; but 
it will be seen that it crosses backwards and forwards with 
no approach to any order or law.” 
But it seemed to me on inspecting the diagram that on 
the average the number of apprehensions for drunkenness 
increased considerably towards the right hand of the diagram 
where the public houses were fewest in proportion to the 
population. To see if this was really the case I grouped 
the numbers together in the following wav. I took the 
mean of the numbers of persons to each apprehension for 
drunkenness on the first twenty towns, and put a mark on 
the diagram opposite the middle town of the twenty at 
a height representing this mean; then the mean of the 
twenty towns from the second to the twenty-first, and put 
a mark opposite the middle town of the twenty to repre- 
rent this mean ; then the mean of the twenty towns from 
the third to the twenty-second, and so on. Running a curve 
