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ing up such a Table as is wanted. But in point of fact the rate is not constant; and it would be unsafe, therefore, of application to any but very short intervals. The variation of rate and its behavior under different combinations that its calculation is susceptible of, will be best seen by an example taken from the census-returns for the several years of the whole population of the United States; as under Years, . 1790. 1800. 1810. 1920. 1830. 1840. Population, 3.929.827 5.305.925 7.239.814 9.638.131 12.366.920 17.068.666
The rate per centum per annum corresponding to this progressive inerease of population, and taking each term successively as the principal, (which is the simplest combination) appears respectively, as under
Years 1800. 1810. 1920. 1830. 1840. 1850. From 1790,
3,043 3,102 3,036 3,010 2,981 2,703 per cent. per annum. 1800,
3,156 3,029 2,997 2,964 1810,
2,903 2,917 2,900 1820,
2,931 2,899 1830,
2,501 Means: 3,043 3,129 2,9592,963; 2,922 The line of means shews the comparative constancy of the rate; which, although it is increasing up to 1810, is yet seen afterwards slowly to diminish. This is more emphatically accused by the numbers in the column under 1850; which represent the ordinate for that year, the curve of the population being supposed to sweep in a regular manner, and the ordinates for the other census-years being taken first in the horizontal column of 1790, and next in the vertical one of 1840, and in both cases using all five terms for the interpolation of the sixth. If we abandon the census of 1790 as having been made upon inadequate observation, and use the last four terms of the line of means, a similar interpolation would give 2,734 per cent. per annum as applicable to the period from 1840 to 1850. Although it is possible that this may be found not very far from the truth, still, as I have already said, a period of 10 years in a territory so extensive and so subject to perturbing influences as ours, is rather too long to be governed by any one uniform rate; and other more unexceptionable means should be resorted to for expanding this series.
If we apply, in the mean time, the same method to the census of Baltimore, we shall find it evidencing similar results and measuring itself through successive eras by a slowly-diminishing geometrical ratio. I have found it advisable, however, to disregard the census of 1790 and 1800, because of their admitted uncertainties; and I have had no opportunity of resort to the State Department, where possibly the uncertainty might be ascertained and removed. Taking then the returns for 1810 and onwards, we have as under: Years,
62.738 60.625 102.313 129.599 The number representing the probable population for 1850 has been deduced from the others by a very expeditious and easy method of In
terpolation, which I have explained in detail elsewhere.* Calculating,
1920. 1830. 1840. 1850.
per cent. per annum. 1920,
2,5401 2,4755 1930,
2,4656 3,0233 2,66794 2,5152; The actual rate from 1830 to 1840, as found here, will, if continued to 1850, give a result for the population but slightly differing (zotoo nearly) from the preceding statement. The coincidence of these independent methods, authorises the more confidence in their results. The rate here placed under the year 1850, arises from a direct interpolation upon the three terms in the column of 1840; it is given among other things to indicate that unless some material change shall have taken place in the elements of our population, or in their modes of affection, ils rate of progress is on the increase compared with the last ten years preceding 1910. The change, however, and its influence can be but slight, since we have for the population in 1850, by direct interpolation, .
129.899 souls. by the actual rate in 1840,
129.830 66 and by the partial rate, above
130.530 Upon such a concurrence, I think it quite safe in calculating the population under the respective years of the Table to be given presently, not only to use the index of 1840 for the period from which it has been derived, but to extend it over the succeeding one. This, although not theoretically so proper under other circumstances, recommends itself here by dispensing with lengthened and laborious calculations; while the amount of error which it introduces in the absolute numbers for population hardly affects the fraction representing the proportionate mortality. In point of fact, such error at its extreme is only appreciable in the third place of decimals. For the period preceding 1830, however, in order to avoid the unsymmetrical break which would have occurred at that epoch in the annual difference of population, it was necessary to interpolate each successive term by the method already mentioned. With these explanations, the Table itself may now be presented as follows: Table of the Population and of the absolute and relative Mortality in Baltimore
for the years from 1826 to 1848, inclusive. Years. Population. Absolute No. of Deaths.
Living =1. 1926, 73.132
1 in 38,1
0,0200 152, 76.811
0,0259 1831, 82.569 2308
• Silliman's Journal: Sec. Ser. No. 19. p. 14, ete.
0,0267 The columns of relative mortality in this Table shew very capricious variations. But one observation may be made upon it, of interest to the community; viz. that since 1845, the mortaliiy has been above the average of the whole twenty-three years, and has been for each of the last six years in a continually increasing ratio. That this result is not an apparent one only, which may arise from a possible error in the annual population in the sense of under-rating it, (as might be argued from the manifest improvement shewn in 1840 above 1830, both of which were census-years, and therefore more reliable, it may be presumed, in the numbers for population) will be manifest by dividing the whole period into groupes of nine years, the smallest number that can be symmetrically arranged, so that each groupe may contain the elements of a census-year. Thus arranged we have Average Mortality for 9 years from 1926 to 1834 inclusive, 1 in 35,03
1 in 39,21 1840 to 1848
. 1 in 39,47 The increased rate of mortality for the last period is equally observable in this as in the general statement; though of course the differences become less strongly marked in proportion to the number of groupes into which the whole term is divided. And in comparing the apparent improvement in the last period above the first, we must have regard to the fact that this first period includes two years of an epidemic-the cholera.
Should we consider it as less important to include a census-year in every groupe, we may arrange the whole period symmetrically into five groupes of 5 years each, with the following results :
1833 to 1841
* These were the years of the Cholera. The victims recorded in 1832 were in all 853; leaving 2719 as the mean mortality of the year, which corresponds to a proportion of 1:31,1 a rate not materially different from that of 1847.
1826–1830, Average Mortality,
1 in 42,5 1830–1934,
1 in 33,5 1835–1939,
1 in 39,2 1840–1944,
1 in 42,3 1844-1843,
1 in 34,7 From this, one might infer that the rate of mortality was subject to circulating periods, at the end of which would be presented again the same factor nearly which occurred at the beginning. Thus, the factor for 1840–44 is almost identical with the rate which governed in 1826, fifteen years before. Such recurrences will be found justified, within certain limits, in a comparison of the general table. Is there any thing in the laws of human existence, by which the mortality of communities is connected with such a periodicity ? The observations which are here given are of course far too restricted in time, number and place to afford any satisfactory answer to this question. But so far as an affirmative can be borne out by the analogy of individual life, it may be observed that this period of fifteen years coincides with all the crises in the Table of Mortality. For instance, at 15 years after birth, the ordinates of the curve of life (such ordinate being the reciprocal of the number dying out of a constant number at every age) have attained their maximum; thenceforward they diminish, the curve becomes of contrary flexure and finds another maximum at 30 years. From that point they go on constantly diminishing, but at 45 there is a stationary node where the flexure is again reversed; and finally at 60 and 75 years there appears to be nodes of retardation where the march of mortality is sensibly disturbed. I regret that neither the character of this paper nor the vehicle through which it is communicated, will allow me to dilate upon this point, which, if proved, will lead to a highly important generalization; or to present graphically the properties and peculiarities of the curve of life, that I have indicated. I will confess only further that, upon what has been said as well as from other considerations, I shall expect the average mortality of the next five years to be less than that which has been just found for 1844–48, and nearer approaching the rate that governed in 1835–39.
As my object here is only to present facts and plain inferences from them, I shall not speculate at any length upon circumstances which may have contributed materially to the sad disparity in the rate of mortality for the last five years ;-) mean the influx of emigrants not elevated in social caste from other countries, and the discomfort, disease, excess, and consequent mortality in that portion of added population. According to the formula upon which the column of population in the general Table has been constructed, the amount of the immigrant increase of population for any year, is based strictly upon the experience of all the years preceding; and no extraordinary increase from such a source has been or can be assumed or allowed for. Nevertheless, it is probable from other considerations which do not submit themselves to calculation, that such extraordinary increase may have taken place in the last two years, and the numbers representing the aggregate annual population may be to that extent erroneous. There are no means within my reach of testing this; I have no list of the arrivals in this port of immigrants during the period referred; nor, if I had, is there any indication or ascertainment of the ultimate sojourn or destiny of persons so arriving. All that can be done is to give the extreme probable error of the Table; which may be arrived at by applying the mean factor (7) of mortality. This factor is derived from a reasonably long experience and, if our populaton were stationary or increasing only by its own fecundity, might be very safely relied upon to give, when divided into the absolute number of deaths, the actual aggregate of the population. So divided, it would result in a population for 1818 of 158,570 souls; the difference between which and the number for the same year in the Table (34,776) shews the utmost probable amount of the immigrant population. That this amount should have been 35,000 souls even for the last five years, I confess I doubt; or rather, I disbelieve: and I apprehend that the census of 1850 will shew the Tabular number as it stands to be not materially in error.*
The mean factor for mortality corresponds with what might be expected from the geographical position of Baltimore-at least from that element of position, Latitude, by which climate is chiefly affected—compared with other cities. In illustration of this, I have arranged the following Table of the principal cities of Europe in the order of their latitude, and annexed to each (in view of the discrepancies of returns for different years) the maximum and minimum of its mortality according to the various statements that have been given. I include in this only one on the continent of America; the statistics of others are not accessible to me. I the rather hope that this research of mine may stimulate other enquirers with better means, to investigate the mortality of the other principal cities in the United States at least.
Of course, the comparison is to be made only between cities; and, if possible, between such as have nearly equal populousness. For it is admitted that other things being equal, the mortality of rural districts is always less than of their metropolis and towns. There are a few ex
a ceptions to this, which only tend to confirm the rule. Thus for instance, five-sevenths of the city of Rome (or perhaps it might be said, the whole city) enjoys a higher freedom from mortality than the adjoining Campagna. But this is plainly to be accounted for; and the unhealthiness of the Campagna and the proverbial fatality of the Pontine Marshes (although both districts may in one sense be said to be in a state of nature) are attributable to circumstances that are justly to be considered artificial, i. e. controllable by the skill and artifice of man.
*Since writing the above I have received the following information; which does not materially change the view of the text.