Frequently the statement is made that business methods should be applied to the conduct of municipal affairs. While private and municipal corporations differ in the respect that the former aim to make money while the function of the latter is to spend it, to both should be applied the same principles of financial economy. Just as in a private corporation the earnings, expenses, and resources must be constantly watched that its affairs may be conducted economically and plans made for the future; so must the financial condition of a municipality be studied, its probable revenues and expenditures determined, in order that its growth may be intelligently understood and its future properly provided for. Recently there was felt the need of some means of measuring the growth, in finances and population, of the City of Boston, Mass. At the request of the Mayor to the City Engineer, the writer, assisted by other , employees of the Engineering Department of the City, undertook the present investigation. Unless the conditions be radically changed, the growth in the future will continue along the same course that has been followed in the past. The aim of the present investigation is to determine what this law of growth has been. From a study of the sta tistics of population, polls, valuation, income, expenditure, and net debt, for a considerable number of years, formulae have been deduced and curves plotted which indicate what future growth may be expected along these lines. DATA AND SCOPE. In every case this study has been made with reference to the area, 46 square miles, included within the present limits of Boston. It deals, therefore, not alone with the original Boston, but also with those cities and towns which were subsequently annexed, viz.: Roxbury, Dorchester, West Roxbury, Brighton, and Charlestown. As Charlestown and Dorchester sustained important losses of territory prior to their annexation, the statistics of these places have been carefully studied and revised to apply as nearly as possible to those areas which subsequently became parts of Boston. There being in the other towns no changes of area materially affecting the total results, the statistics of Roxbury, West Roxbury, and Brighton have been used without revision. The data used in the calculations are given in tables attached hereto. Tables I. to W. inclusive (population, polls, and valuation) were compiled by employees of the Engineering Department from an examination of original records, reports, and maps on file in the Massachusetts State Library and the offices of the Assessors of Boston and the Secretary of the Commonwealth. Table VI. (income and expenditure) was prepared by the Statistics Department of the City, and the data contained therein will be found in the forthcoming “Special Publication No. 5’ of that Department. Table VII. (net debt) is taken from the report of the City Auditor for 1899–1900, page 250. Where it has been necessary to estimate data of population, polls, and valuation, the number of significant figures given in the tables (I. to W. inclusive) roay be used as a measure of the accuracy of the estimate. In such cases it is 'elieved that all significant figures except the last are correct; and that the error, if any, in the last place will usually be slight. DERIVATION OF FORMUL.AE. The formulae have been derived by the method of least squares. They have the general form in which X is the quantity sought, t is the time in years from 1900 (being negative prior, and positive Subsequent, to that year), and A, B, and C are constants to be derived mathematically. These formulae are the equations of curves parabolic in shape and concave upward, this being the form which appears to fit the data most closely. POPULATION AND POLLS. The statistics of population and polls, given in Table II., are shown graphically on Plate A. First Formula for Population. — The formula, as determined from the actual population in twenty census years, from 1790 to 1900, inclusive, is as follows: This formula, while being the best of its form that can be derived from the observations used, is not closely in agreement with the actual populations of the last fifteen years, and when used to predict future population it gives results obviously too small. The explanation of this is to be found in the effect of the Civil War, and the subsequent business depression, in retarding the growth of the City. The setback appears to have affected the censuses of 1865, 1870, 1875, 1880, and, to some extent, even that of 1885. The first formula for population should not be used for predicting growth in the future. Formula for Polls. – The first population formula having proved unsatisfactory, attention was next directed to a study of the assessed polls. For this investigation the polls in each year from 1822 to 1900, inclusive, were available, giving 79 observations, from which was derived the formula Comparison of the curve plotted from this formula with the actual polls shows that, while as we should expect there is some deviation between the two during the Civil War period, in general the curve and the actual polls are in close agreement. Especially is this true during the past twenty years, during which time the computed and actual polls in no case differ by more than about 2 per cent. while the average differ. ence is 1.2 per cent. It is thought that for the next few years this formula may be used for estimating polls with a fair degree of accuracy. The results predicted by it will probably be slightly less than the actual polls as subsequently found. Relation Between Population and Polls. – A satisfactory formula for polls having been derived, a study was made of the ratio of population to polls whenever (as in census years) actual comparison of the two was possible. It was found that this ratio varied considerably in the seventy-five years considered. It was highest, as one would expect, in 1865, when the proportion of adult males had been reduced by the Civil War. It is surprising to observe, however, that while prior to the war the population was from 4% to 5 times the number of polls, since 1865 the ratio has been steadily diminishing until in 1900 it reached a minimum of 3.37. This means that the number of adult males is increasing at a faster rate than the increase in population; and that while in 1850 out of every 100 population there were only 21 men, in 1900 the adult males constituted nearly 30 per cent. of the total population. It would be interesting to study the causes of this increase in the percentage of men. It is not that men are gradually outnumbering women, for the percentages of males and females in the population of Boston are substantially the same to-day as fifty years ago. This change appears even more pronounced when it is remembered that prior to 1843 poll taxes were assessed on all males above 16 years of age, while since that date the poll assessment has been of all males over twenty. Assuming, as we may, that the assessment of polls in the past was reasonably accurate and complete, we are forced to the conclusion that children form a smaller part of the population of Boston to-day than they did 50 or 75 years ago. Among the causes contributing to this result the following are suggested: 1. An increase in the age of marrying, leaving a greater number of young single men (and women) in the community. 2. A decrease in the size of families, a family usually having fewer children to-day than fifty years ago. 3. The probable fact that, of the men finding employment in the City, those who are single generally live within the City limits, while men with families are inclined to seek residence in the suburban cities and towns. That the third reason may be true to some extent is indicated by the following table” comparing the population and polls in 1900 in (a) Boston, (b) the metropolitan district including all cities and towns within 10 miles of the State house, and (c) the whole State: Ratio Percentage Population Polls Population Of Polls in 1900. in 1900. to to Total POllS. Population. Boston . . . . . . . . . . . . . . . . . . . . . . . . . . 560,892 166,354 3.372 29. 66 Metropolitan District.......... 1,128,704 323,709 3.487 28.68 Massachusetts. . . . . . . . . . . . . . . . . . 2,805,346 778,911 3. 602 27.77 In the present investigation there was neither time nor place for an extended study of social conditions as here indicated. Considering only the conditions in Boston as they actually existed, it is found that, |