NOTES AND MEMORANDA ?ESTIMATION OF i:)OPULATIONS Two Succssv IN THE INTERVAL BETWEEN C.NSVS.S PROBABLY few will be disposed to deny the statement that an accurate knowledge of the number of the people is the essential basis of all statistics. The census gives us this knowledge at more or less distant intervals, possibly in some countries not so accurately in our own country certainly not so frequently as might be desired; but in all cases in the intervals between the recurring census years we are thrown back upon the poor substitute of estimates. In England, as is well known, the population is estimated each year on the hypothesis that the geometrical rate of increase prevalent during the ten years immediately preceding the last available census remains the same during the next decade: that is to say, that a number of contributing causes, each one of which is known to vary, will combine to produce a constant result. Is this method a pr/or/ a rational one ? Our officials tell us that for large populations such as that of England and Wales it gives very .approximately correct results; moreover, that it is the best practicable method. What do the facts tell us ? In the General Report on the Census of England and Wales, 1881 (p. 6), the rate of increase in three periods of ten years is given as follows: 1851-61 ......... 11'93 per cent. 1861-71 ......... 13'19 ,, 1871-81 ......... 14'36 ,, Surely these figures alone are sumcient to prove that the rate of increase has not been uniform in the past, and therefore the hypothesis has no valid foundation. Had the population, indeed, increased between 1871 and 1881 at the same rate as in the preceding decade it would have amounted to only 25,708,052, whereas actually it was found to exceed that number by 266,387. In the same place the report points out that the population of England and Wales, as estimated by the natural increment (or excess
