although the ratio of population to polls varied considerably for some years after the Civil War, the effects of the latter appear to have been largely overcome by 1885, from which date to 1900 population and polls bore a nearly constant, though slightly diminishing, ratio, one to the other. Using: the observations of 1885, 1890, 1895, and 1900, a formula has been determined for pre dicting the ratio to in the future. The formula is R = 3.430 – 0.0065 t Second Formula for Population. — Since the estimated population in any future year should equal the estimated polls multiplied by the estimated ratio o for that year; by multiplying together the formulae for polls and for this ratio (and neglecting the term containing to) we obtain the second formula for population, viz.: If accurate, this formula should give results closely in agreement with the actual populations in 1885, 1890, 1895, and 1900. That this is the case is shown by the following table in which it is seen that the actual and computed populations differ each time by less than one per cent. : Population YEAR. Péon do. by Difference. rous Of Boston. Formula. Difference. 1885 . . . . . . . . . . . . 390,393 391,495 +-1099 +0.28 1890 . . . . . . . . . . . . 448,477 444,570 —3907 –0.87 1895 . . . . . . . . . . . . 496,920 500,745 +3825 +0.77 1900 . . . . . . . . . . . . 560,892 560,020 — 872 —0.16 Other formulae for population have been deduced under various conditions, but none of them agree so closely with the actual populations from 1885 to 1900 as the second. Believing the growth of population in the fifteen years named to have been normal, the writer offers this second formula as the one to be used in predicting population for several years to come. vaLUATION. Table IV. shows the total assessed valuation of Boston in each year since its incorporation as a city in 1822. These values are plotted on Plate B. It will be seen that the valuation increased at a fairly uniform rate from 1822 to the Civil War and from about 1880 to the present time. During the war and for nine years thereafter it rose at a rapid rate, reached a maximum value in 1874, and fell rapidly from 1875 to 1879, after which it rose slowly for five or six years. This sudden rise and subsequent decline are accounted for by the fact that in this period values were made upon a different monetary basis from that existing before the war and after 1879, gold during this time being at a premium. Not until 1885, six years after the resumption of specie payments, do Boston valuations appear to have entirely recovered from the financial disturbance and to have reached once more a normal growth. First Formula for Valuation. — The first formula for valuation has been determined by using the actual valuations for the years 1822 to 1860 and 1881 to 1900, inclusive, rejecting the valuations for the twenty years 1861 to 1880 on account of the variation in the monetary basis during that time. The formula is W = [1075.9-i-25.08 t-i- 0.153 to x $1,000,000. It will be seen by reference to the corresponding curve on Plate B that this formula does not agree well with the growth of valuation from 1885, since which time the actual valuation has been increasing at a faster rate than the formula would indicate. Considering the set-back the City sustained in consequence of the Civil War this result was to have been expected. The first formula for valuation, therefore, should not be used in predicting the growth of the future. / 200 000 A 200 000 FIRST CURVE FOR POPULATION determined by observations from 1790 to 1900. SECOND CURVE FOR POPULATION obtained by multiplying Curve for Polls by Assumed Curve, showing Ratio of / /OO (200 / /90 000 CURVE FOR POLLS determined by observations from 1822 to 1900, P = | 63 27O + 3856 t + 25.4 to / OOO OOO / 000 000 ASSUMED CURVE, showing Ratio of Population to Polls, determined by observations from 1885 to 1900. 3OO COO 300 000 In all curves t expresses time in years from 1900. ACTUAL POPULATION o T. I so shown thus: O /5. ACTUAL POLLS . o o o * o , shown thus: O &OO OOO 30 3OO OOO ACTUAL RATIO = **ś . m : shown thus: • MARC H., 19 O1. 700 000 700 OO62 /3 6oo ooo “o 600 000 32%) ao? 2200 000 200 OO6) 300 00 (20 OOO 3OO 6%X) 200 (2/20 2OO ©o /OO OOO /OO 000 O O Second Formula for Valuation. — Assuming that the valuation has increased at a normal raté since 1885, by using the valuations from 1885 to 1900, inclusive, there has been derived a second formula: W = [1112.7 -- 30.7 t + 0.16 to x $1,000,000. This formula gives results in close agreement with the actual valuations of that period, the greatest deviation between computed and actual valuation for any year being less than two per cent. and the average difference of the two being 0.91 per cent. The second formula should be used in predicting future valuations. IN COME, EXPENDITURE, AND NET DEBT. As stated at the beginning, this investigation deals throughout with the territory constituting the present area of Boston. It having been impossible, so far, to obtain statistics of the income, expenditure, and debt of Roxbury, Dorchester, Charlestown, West Roxbury, and Brighton prior to their annexation to Boston, the data along these lines commence with the year 1874, when all annexations had been made. Prior to 1891 the financial year of the City began May first. In 1891–92 the financial year consisted of but nine months, viz., from May 1, 1891, to January 31, 1892. Beginning with 1892, each financial year has commenced on the 1st of February. As the income and expenditure for the nine months constituting the financial year 1891–92 cannot be made to fairly represent the income and expenditure of a whole year, they have been omitted from the calculations. e The statistics of income and expenditure are given in Table VI., and those of net debt in Table VII. All data used in the computations are plotted on Plate C. The total income has been divided into (a) Taxes and other income. (b) Income from loans. The former consists of all moneys received from taxes, licenses, water-rates, assessments and better |