HC Deb 09 July 1928 vol 219 cc1871-3W

asked the Minister of Health whether, in order to facilitate the studies of Members, he will give the algebraic formula of which paragraph 23 of Cmd. 3134 is a paraphrase?


The formula is as follows:—

Let p = the population of a county in the standard year as estimated by the Registrar-General.

Let c = 50 or the number of children under five years of age per thousand of the population, whichever is the greater.

Let a = 10 or the rateable value in £ per head of the population according to the valuation list in force on the 1st October, 1929, whichever is the less.

Let u = 1.5 or the percentage of unemployed men calculated as explained in Cmd. 3134, whichever is the greater.

Let m = the number of persons per mile of public road.

Then (1) if m is greater than or equal to 100, the weighted population is



(2) if m is less than 100 the weighted population is



In the case of London and the county boroughs, the last term in the second bracket is always taken as zero, as there is no weighting for low density of population in those cases.

The following example illustrates the working of the formula. The figures are those for the Administrative County of Durham (vide page 32 of Cmd. 3134).


Elements of the formula.
(a) Number of children under five years of age per 1,000 of the population 113
(b) Estimated rateable value per head of population when de-rating is in operation £2.95
(c) Percentage of population represented by number of unemployed insured men (estimated average of three years) 5.2
(d) Estimated population per mile of public roads 444
(e) Estimated population (in 1926) 996,700
Calculation of weighted population.
(i) Estimated actual population 996,700
(ii) Increase for children of 126 per cent. (113 exceeds 50 by 63 which is 126 per cent. of 50) 1,255,842
(iii) Increase for low rateable value of 70.5 per cent. (£2.95 is £7.05 below £10, and 7.05 is 70.5 per cent. of 10) 702,674
The increased population of 2,955,216 is further weighted by:
(iv) a percentage of 37 for unemployment (5.2 exceeds 1.5 by 3.7, and 10 times 3.7 is 37) 1,093,430
(v) a percentage of 11.3 for low density of population (444 exceeds 100; the percentage increase is therefore 50/444 × 100, i.e., 11.3) 333,939
Total weighted population 4,382,585

A grant of 31.35 pence per head of a total weighted population of 4,382,585 is equivalent to a grant of 137.8 pence per head of an actual population of 996,700.