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 U. S. SANITARY COMMISSION. 
 STATISTICAL BUREAU. 
 
 AGES 
 
 OF 
 
 U. S. VOLUNTEER SOLDIERY. 
 
 NEW YORK 
 1866. 
 

 University Press : Welch, Bigelow, & Co., 
 Cambridge. 
 
Cambridge, January, 1866. 
 
 Dear Sir, — 
 
 Inclosed is my Report on the Ages of Volunteers in the late war. 
 The general results were communicated, by permission, to the 
 National Academy of Sciences at its session in August last, and 
 tins Report was read before the Commission in November ; but 
 the Appendix, concerning the Ages of a Population in general, 
 has been prepared since that time. 
 
 For most of the troops comprised within the limits of the 
 present discussion, no descriptive muster-rolls exist. The Ages, 
 Nativities, and Statures of those troops whose descriptions are 
 on record will soon be made the subject of another Report. 
 
 I am, dear Sir, 
 
 Very respectfully and sincerely yours, 
 
 B. A. GOULD, 
 
 Actuary U. S. Sanitary Commission. 
 
 John S. Blatchford, Esq., 
 
 General Secretary U. S. Sanitary Commission. 
 
CORRIGENDA. 
 
 Pa<rc 6, line 23, for face read force. 
 
 " 10, " 19, " 28.4843 " 28.4850. 
 
 " 30, " 28, " Column 9 " Column 3. 
 
 39, " 24, " one million •' one hundred thousand. 
 

AGES 
 
 UNITED STATES VOLUNTEER SOLDIERY 
 
 1. Introductory. 
 
 On taking charge of the Statistical Department of the United 
 States Sanitary Commission, in August, 1864, it was found that 
 considerable progress had been made in collecting the ages of the 
 soldiers of our volunteer regiments, — an investigation which had 
 been suggested and commenced by Mr. Elliott, the accomplished 
 and skilful statistician, who, not very long before, had relin- 
 quished the direction of this Bureau of the Commission. 
 
 Although the best use to be made of the materials appeared 
 somewhat uncertain, it did not seem proper to discontinue in- 
 quiries already so far advanced ; and the large experience of Mr. 
 Elliott in matters connected with vital statistics gave assurance 
 that valuable as well as interesting results were likely to be 
 deduced from a thorough study of these data. 
 
 The collection of these materials was therefore continued and 
 completed, by means of the muster-rolls on file at the War De- 
 partment in Washington, to which access was courteously af- 
 forded by General E. D. Townsend, Acting Adjutant-General, and 
 Colonel Samuel Breck, who was in charge of the rolls. Tables 
 have thus been formed for twenty-seven States, Territories, or geo- 
 graphical groups, exhibiting the number of men at each year 
 of age in the volunteer organizations, at the time of their mus- 
 ter into the service of the United States. The officers are tabu- 
 lated as a distinct class ; and the three arms of the military 
 service — infantry, cavalry, and artillery — have been treated 
 separately. 
 
Z AGES OF VOLUNTEERS. 
 
 The original collection of the materials was principally made 
 by Mr. T. J. O'Connell, until lately the efficient and accurate 
 chief clerk of the Statistical Department, and was completed by 
 Mr. E. A. Wilson. The tabulation has been made by Messrs. 
 O'Connell, Wilson, A. A. Brooke, and John N. Stockwell; 
 and the greater part of the computations has been performed 
 by Mr. Stockwell alone, with great care, perseverance, and 
 ability. 
 
 The recruits who joined these original regiments after their 
 first organization and acceptance into the national service are 
 not included ; and the limits of the investigation have excluded 
 all drafted men, substitutes, &c. Moreover, many regiments be- 
 longing within these limits are omitted, because organized since 
 the collection of the data for the States to which they belong ; 
 but the number of these is comparatively small, and inadequate 
 to exert any sensible effect upon the results. The degree of com- 
 pleteness may be seen by the following table, which shows the 
 number and date of the latest regiment included in the collection. 
 
 Arkansas 
 
 2d Infantry, 
 
 latest. 
 
 Mississippi 
 
 Marine Brig. 
 
 only organ'n 
 
 California 
 
 4th 
 
 tt 
 
 1862, Feh. 
 
 Missouri 
 
 34th Infantry 
 
 1862, Dec. 
 
 Connecticut 
 
 28th 
 
 " 
 
 1862, Nov. 
 
 Nevada 
 
 1st 
 
 " 
 
 1864, June 
 
 Delaware 
 
 2d 
 
 " 
 
 1861, Dec. 
 
 N. Hampshire 1 8th 
 
 " 
 
 1864, Sept 
 
 Illinois 
 
 131st 
 
 " 
 
 1864, June. 
 
 New Jersey 
 
 25th 
 
 u 
 
 1862, Sept 
 
 Indiana 
 
 115th 
 
 a 
 
 1863, Aug. 
 
 N. Mexico 
 
 4th 
 
 " 
 
 1863. 
 
 Iowa 
 
 48th 
 
 tt 
 
 1865. 
 
 New York 
 
 177th 
 
 " 
 
 1863, June. 
 
 Kansas 
 
 15th 
 
 " 
 
 1863. 
 
 Ohio 
 
 128th 
 
 " 
 
 1863, Aug. 
 
 Kentucky 
 
 52d 
 
 " 
 
 1864. 
 
 Pennsylvania 
 
 t 155th 
 
 " 
 
 1863, Jan. 
 
 Louisiana 
 
 N. 0. 
 
 Vols. 
 
 1864, May. 
 
 Rhode Island 12th 
 
 " 
 
 1862, Oct. 
 
 Maine 
 
 28th Infantry 
 
 1864. 
 
 Tennessee 
 
 8th 
 
 " 
 
 1864. 
 
 Maryland 
 
 10th 
 
 " 
 
 1864, June. 
 
 Vermont 
 
 16th 
 
 " 
 
 1862, Oct. 
 
 Mass. 
 
 59th 
 
 " 
 
 1864, July. 
 
 W. Virginia 
 
 15th 
 
 " 
 
 1862, Sept. 
 
 Michigan 
 
 27th 
 
 " 
 
 1864, Aug. 
 
 Wash. Terr. 
 
 1st 
 
 tt 
 
 only reg't. 
 
 Minnesota 
 
 10th 
 
 " 
 
 1864, Aug. 
 
 Wisconsin 
 
 53d 
 
 <t 
 
 1864. 
 
 The total number of volunteers whose ages have thus been 
 investigated is 1 049 457, of whom 1 012 273 were enlisted men, 
 and 37 184 were commissioned officers. All except 1^ per cen- 
 tum (.01495) of the men, and 31 per centum (.0331) of the offi- 
 cers, were between the ages of 18 and 46 years at the date of 
 their enlistment or commission. Those beyond these limits have 
 not been included in the determination of the general formulas, 
 
AGES OF VOLUNTEERS. 3 
 
 so that these depend upon the statistics of ages for 1 032 600 men, 
 of whom 35 953 were commissioned officers.* 
 
 The results have proved amenable to law in a higher degree 
 than I had ventured to anticipate. Residual discordances exist, 
 of course, between the numbers for each year of age, as derived 
 from the tabulated records, and those indicated by the general 
 formulas deduced from the whole series ; yet where these dis- 
 cordances attain any essential magnitude, they may almost in- 
 variably be made to yield instructive and useful information. 
 
 The results attained, for that portion of the population who 
 thus rushed to the field at their country's call, naturally suggest 
 analogous inquiries regarding the white male population of the 
 United States, and especially relative to the population of that 
 portion of the country which furnished the volunteers under con- 
 sideration. And it was not until after many unavailing efforts 
 to obtain information as to the distribution of our population by 
 ages, that the great deficiency of our knowledge of the facts and 
 laws relative to this very important subject became manifest. 
 
 The only published attempt, of which I am aware, to classify the 
 population of the United States according to years of age is very 
 crude, and the method pursued yields results quite at variance 
 from the truth. The only trustworthy facts are contained in the 
 summaries of the census-returns ; and the groups into which the 
 population is there divided are altogether too large to permit the 
 desired laws to be deduced with ease. It is earnestly to be hoped 
 that in future census-publications the groups may be so made as 
 to include intervals of age not greater than five years. 
 
 It thus became important, if only for the sake of comparison 
 between the age%of the volunteer troops and that of the popula- 
 tion whence they sprung, to subject the census of 1860 to a simi- 
 lar discussion. And I cannot but think that the results elicited 
 might be advantageously employed, so far as they apply and 
 extend, for the life-tables of our insurance and annuity offices. 
 The life-curve for our American population is clearly diverse 
 from the curve on which the present English tables are based ; 
 
 * The prescribed limits of military age at the commencement of the rebellion were 
 18 and 45 years ; but the large proportional number at the age of 45 seems to indicate 
 that the law was so interpreted as to permit the acceptance of volunteers whose age at 
 their last birthday did not exceed 45 years. 
 
4 AGES OF VOLUNTEERS. 
 
 and it is a source of regret that the proper limits of the present 
 investigation forbid its extension into the tempting fields of in- 
 quiry which their comparison suggests. 
 
 The fact which first attracts attention among the results of this 
 research is the marked diversity between the distribution of the 
 ages of officers and that of the enlisted men. Each follows a 
 clearly manifest law ; in each case the law is deducible with close 
 approximation to the truth ; so also is the law governing the ages 
 of our population ; yet each of the three is utterly different from 
 the other two. The sources of the diversity may well be made 
 the object of careful research, and not without a reasonable prob- 
 ability of useful results. Certain discordances between the re- 
 corded and the computed numbers for a few particular ages will 
 be considered hereafter. 
 
 2. Ages of the Unlisted Men. 
 
 The grand total of the rank and file of the volunteers whose 
 ages are included in this discussion is shown in the following 
 tabular view, which exhibits the recorded age at last birthday for 
 the entire number ; although, as already stated, those under 18 
 or over 45 (last birthday), 15 626 in all, have been excluded 
 from the general discussion. These excluded cases represent two 
 classes, viz. the boys, chiefly drummers, musicians, &c, and the 
 men who, although past the legal age, were so sturdy or earnest 
 that the enrolling officers did not, at that time of great national 
 peril, feel justified in insisting on an absolute compliance with 
 the legal qualifications. 
 
 In the column entitled " Miscellaneous " are included all those 
 organizations which do not belong strictly within the three prin- 
 cipal arms of the military service, such as Engineers, Sharpshoot- 
 ers, Mounted Infantry, Coast Guards, Marine Brigades, &c, to- 
 gether with a few regiments or battalions for which the statistics 
 were received after the special computations for Infantry, Cavalry, 
 and Artillery had been completed, so that their incorporation with 
 these would have required a repetition of the calculations without 
 producing any essential change in the result. 
 
AGES OF VOLUNTEERS. 
 
 TABLE I. 
 
 Classified Summary of Enlisted Volunteers. 
 
 Age 
 
 at last 
 
 birthday. 
 
 ACTUAL NUMBER OF MEN. 
 
 Total 
 
 at each year 
 
 of age. 
 
 Infantry. 
 
 Cavalry. 
 
 Artillery. 
 
 Miscellaneous. 
 
 13 
 
 113 
 
 5 
 
 
 
 9 
 
 127 
 
 14 
 
 288 
 
 15 
 
 2 
 
 25 
 
 330 
 
 15 
 
 636 
 
 49 
 
 21 
 
 67 
 
 773 
 
 16 
 
 2053 
 
 232 
 
 61. 
 
 412 
 
 2758 
 
 17 
 
 4653 
 
 638 
 
 226 
 
 908 
 
 6425 
 
 18 
 
 103420 
 
 15013 
 
 5400 
 
 9642 
 
 133475 
 
 19 
 
 71226 
 
 9767 
 
 3439 
 
 5783 
 
 90215 
 
 20 
 
 56238 
 
 7864 
 
 2627 
 
 4329 
 
 71058 
 
 21 
 
 75978 
 
 12081 
 
 4416 
 
 4661 
 
 97136 
 
 22 
 
 57485 
 
 9096 
 
 3107 
 
 3703 
 
 73391 
 
 23 
 
 48954 
 
 7806 
 
 2759 
 
 3198 
 
 62717 
 
 24 
 
 40852 
 
 6361 
 
 2163 
 
 2719 
 
 52095 
 
 25 
 
 36383 
 
 5724 
 
 2012 
 
 2507 
 
 46626 
 
 26 
 
 31292 
 
 4831 
 
 1768 
 
 2352 
 
 40243 
 
 27 
 
 26369 
 
 4192 
 
 1505 
 
 2220 
 
 34286 
 
 28 
 
 27196 
 
 4318 
 
 1525 
 
 2273 
 
 35312 
 
 29 
 
 18833 
 
 2845 
 
 10S7 
 
 1748 
 
 24513 
 
 30 
 
 21937 
 
 3251 
 
 1213 
 
 1959 
 
 28360 
 
 31 
 
 12814 
 
 2053 
 
 796 
 
 2301 
 
 17954 
 
 32 
 
 17038 
 
 2450 
 
 931 
 
 1548 
 
 21967 
 
 33 
 
 13678 
 
 1950 
 
 753 
 
 1598 
 
 17979 
 
 34 
 
 12004 
 
 *1679 
 
 724 
 
 1333 
 
 15740 
 
 35 
 
 14558 
 
 2130 
 
 836 
 
 1456 
 
 18980 
 
 36 
 
 10437 
 
 1541 
 
 702 
 
 1377 
 
 14057 
 
 37 
 
 8782 
 
 1268 
 
 477 
 
 1293 
 
 11820 
 
 38 
 
 10025 
 
 1416 
 
 579 
 
 1326 
 
 13346 
 
 39 
 
 7200 
 
 979 
 
 416 
 
 1001 
 
 9596 
 
 40 
 
 10886 
 
 1441 
 
 649 
 
 1019 
 
 13995 
 
 41 
 
 5634 
 
 822 
 
 320 
 
 659 
 
 7435 
 
 42 
 
 8369 
 
 1199 
 
 535 
 
 826 
 
 10929 
 
 43 
 
 7900 
 
 1079 
 
 533 
 
 828 
 
 10340 
 
 44 
 
 12274 
 
 1851 
 
 796 
 
 1149 
 
 16070 
 
 45 
 
 5509 
 
 954 
 
 289 
 
 260 
 
 7012 
 
 46 
 
 737 
 
 105 
 
 45 
 
 80 
 
 967 
 
 47 
 
 541 
 
 74 
 
 34 
 
 63 
 
 712 
 
 4S 
 
 532 
 
 73 
 
 31 
 
 63 
 
 699 
 
 49 
 
 354 
 
 60 
 
 17 
 
 38 
 
 469 
 
 50 & 
 
 1942 
 
 203 
 
 68 
 
 153 
 
 2366 
 
 over. 
 
 
 
 
 
 . 
 
b AGES OF VOLUNTEERS. 
 
 The relative excess of the numbers at certain particular ages, 
 and the corresponding defect at others, strikes the attention at 
 the first glance. To the former class belong the ages, 21 years, 
 most years divisible by 5 (excepting 20 and 45), and those divisi- 
 ble by 2 ; to the latter class belong most of those years of age 
 whose last digit is 1 or 9. By determining the general law of 
 distribution, we may obtain the measure of this excess, and thus 
 throw light upon the origin of these discordances. 
 
 The following facts are also manifest, or readily deducible : — 
 
 Of the whole number, 1 012 273, about 1 per centum (.0102), 
 were below, and a little more than one half as many (.0052) were 
 above, the limits of military age, interpreted as between the ages 
 18 and 46. 
 
 Of the number 996 647, within these limits, — 
 The average age at last birthday is ... 25.3250 
 
 The average age at time of enlistment is . . . 25.8083 
 The age above and below which the numbers are equal is 23.477 
 There were of the age 18 years . . . .13.27 per cent, 
 under 21 years .... 29.52 " 
 under 25 years . . . .58.34 " 
 under 30 years .... 76.57 " 
 
 The very close accordance of the proportional numbers for the 
 total face of about a million of men from all the loyal States, with 
 those deduced * by Mr. Elliott for less than 51 000 men from the 
 single State of Massachusetts, is very striking. Tables for the 
 individual States and groups of States, herewith presented, unite 
 in corroborating the inference that this distribution is due to no 
 special local influences, but to a general and overruling law, which 
 varies but slightly through widely distant regions of our country, 
 and seems scarcely affected by any influences dependent upon 
 immigration from abroad. 
 
 This law, which was found by Mr. Elliott to hold good also for 
 the Massachusetts troops, shows the number of volunteers (en- 
 listed men, not including officers) at each successive year of age 
 to form a series of which the first differences are in geometrical 
 progression. 
 
 • When the ratio of this geometrical progression is unity, the 
 
 * " On the Military Statistics of the United States of America," Proceedings of the 
 International Statistical Congress, V Session, 1S63, p. 32. 
 
AGES OF VOLUNTEERS. 7 
 
 progression becomes arithmetical ; when, as in the present case, 
 it is less than unity, we have a decreasing rate of change. 
 
 Let this ratio be denoted by h, and the number of men at any 
 
 given year of age be 
 
 Xn = b + c(l-h)h" (1) 
 
 so that the total number at and over that age will be 
 
 s n = a — bn-\-ch n (2) 
 
 in which n denotes the excess of the age above 18 years, at which 
 
 epoch 
 
 s = a -f- c. 
 
 The constants a, b, c, h are to be determined, and we have 
 
 jx Q = c(l— h)% jx n = ch n (l — h)\ j m x mn = ch mn (l — h m y 
 
 whence 
 
 fan _ dmX mn /g\ 
 
 Am. x (m + 1) n 
 
 which enables us to determine h from the most convenient equi- 
 distant portions of the series. 
 
 The variation of the fundamental equation (2) gives for any 
 change in the values of the constants 
 
 &*„ = aa — n^b + h n & + nch n - 1 M, (4) 
 
 by means of which, after an approximate value of h has been 
 deduced from (3), and corresponding values of a, b, c derived 
 from the numerical data for any four years, the corrected values 
 of all four constants may be derived by the method of least 
 squares. 
 
 The total number up to any given age, or the definite sum from 
 x to x n , is evidently 
 
 s - s n = bn + c (1 — A") = 5J* (5) 
 
 so that 
 
 or by (2) 
 
 »+s*"=s( c -s: af ) 
 
 = \ (*» - «)• (6) 
 
 Since the numerical values deduced from the tables belong not to 
 the age n years, but to that age which corresponds to the average 
 
8 AGES OF VOLUNTEERS. 
 
 for all the individuals between n and n-\-l years, the constants 
 deduced hold good also for the series of these mean ages ; the 
 successive annual arguments being really at intervals differing 
 slightly from one year. 
 
 The age t corresponding to this average may be deduced for 
 any year with sufficient accuracy for all practical purposes, by put- 
 ting n — t in the first member of equation (6), and using in the 
 last member the value of s n+i instead of s n , which gives 
 
 -< + ^ = ^( Sn+i -a). (7) 
 
 Similarly we may find the age corresponding to the average for 
 any period of years. For this purpose we replace s n+i in the last 
 member of the equation (7) by 
 
 *(* + *)=« — * *(n + nO + *e(*» + *0 
 
 and the corresponding value of t is the age equivalent to the 
 average of the period included between n and ri. 
 
 Proceeding as above described, and, after the first approximate 
 determination of h, a, b, c, from four conveniently situated and 
 equidistant observed values of s n , obtaining improved values for 
 all four constants by the method of least squares, the formulas 
 derived from the grand total of all the enlisted men of military 
 age as presented in Table I. are these, which express the relative 
 numbers for every ten thousand : — 
 
 x n = -f 77.04 + 1156.0 • 0.85362" 
 
 *„ = 2102.8 — 77.04 n + 7897.2 • 0.85362". 
 
 With these values the fourth and seventh columns of Table II. 
 are computed, the third and sixth columns showing the "ob- 
 served," or recorded numbers, reduced to the same scale ; and 
 the fifth and eighth columns exhibiting the discordances between 
 the calculated and observed values. 
 
 These discordances, although in one sense regular, inasmuch as 
 the larger ones are apparently not the result of so-called accident, 
 or, in other words, of the use of numbers insufficient to eliminate 
 discordances of no palpable significance, are in another sense 
 markedly devoid of regularity, inasmuch as the positive and neg- 
 ative signs alternate freely, and no decided indication seems to 
 exist of a systematic deviation of the general formula. 
 
AGES OF VOLUNTEERS. 
 
 TABLE II. 
 
 Grand Total of Enlisted Men. 
 
 Age 
 
 at last 
 
 birthday. 
 
 Number. 
 
 Proportion 
 giveL 
 
 Observed. 
 
 at and over 
 age. 
 
 Calculated. 
 
 Difference. 
 (C. - O.) 
 
 Propc 
 at givt 
 
 Observed. 
 
 rtion 
 n age. 
 
 Calculated. 
 
 Difference. 
 (C. - 0.) 
 
 13 
 
 127 
 
 
 
 
 
 
 
 14 
 
 330 
 
 
 
 
 
 
 
 15 
 
 773 
 
 
 
 
 
 
 
 16 
 
 2758 
 
 
 
 
 
 
 
 17 
 
 6425 
 
 
 
 
 
 
 
 18 
 
 133475 
 
 10000 
 
 10000 
 
 
 
 1339 
 
 1233 
 
 -106 
 
 19 
 
 90215 
 
 8661 
 
 8767 
 
 +106 
 
 905 
 
 1064 
 
 + 159 
 
 20 
 
 71058 
 
 7756 
 
 7703 
 
 - 53 
 
 713 
 
 919 
 
 +206 
 
 21 
 
 97136 
 
 7043 
 
 6784 
 
 -259 
 
 975 
 
 796 
 
 -179 
 
 22 
 
 73391 
 
 6068 
 
 5988 
 
 - 80 
 
 736 
 
 691 
 
 - 45 
 
 23 
 
 62717 
 
 5332 
 
 5297 
 
 - 35 
 
 629 
 
 601 
 
 - 28 
 
 24 
 
 52095 
 
 4703 
 
 4696 
 
 - 7 
 
 523 
 
 524 
 
 + 1 
 
 25 
 
 46626 
 
 4180 
 
 4172 
 
 - 8 
 
 468 
 
 460 
 
 - 8 
 
 26 
 
 40243 
 
 3712 
 
 3712 
 
 
 
 404 
 
 403 
 
 - 1 
 
 27 
 
 34286 
 
 3308 
 
 3309 
 
 + 1 
 
 344 
 
 355 
 
 + 11 
 
 28 
 
 35312 
 
 2964 
 
 2954 
 
 - 10 
 
 354 
 
 315 
 
 - 39 
 
 29 
 
 24513 
 
 2610 
 
 2641 
 
 + 31 
 
 246 
 
 280 
 
 + 34 
 
 30 
 
 28360 
 
 2364 
 
 2361 
 
 - 3 
 
 285 
 
 250 
 
 - 35 
 
 31 
 
 17954 
 
 2079 
 
 2111 
 
 + 32 
 
 181 
 
 225 
 
 + 44 
 
 32 
 
 21967 
 
 1898 
 
 1886 
 
 - 12 
 
 221 
 
 203 
 
 - 18 
 
 33 
 
 17979 
 
 1677 
 
 1683 
 
 + 6 
 
 181 
 
 185 
 
 + 4 
 
 34 
 
 15740 
 
 1496 
 
 1498 
 
 + 2 
 
 158 
 
 169 
 
 + 11 
 
 35 
 
 1S980 
 
 1338 
 
 1329 
 
 - 9 
 
 191 
 
 156 
 
 - 35 
 
 36 
 
 14057 
 
 1147 
 
 1173 
 
 + 26 
 
 141 
 
 144 
 
 + 3 
 
 37 
 
 11820 
 
 1006 
 
 1029 
 
 + 23 
 
 118 
 
 134 
 
 + 16 
 
 38 
 
 13346 
 
 888 
 
 895 
 
 + 7 
 
 133 
 
 126 
 
 - 7 
 
 39 
 
 9596 
 
 755 
 
 769 
 
 + 14 
 
 96 
 
 118 
 
 + 22 
 
 40 
 
 13995 
 
 659 
 
 651 
 
 - 8 
 
 141 
 
 112 
 
 - 29 
 
 41 
 
 7435 
 
 518 
 
 539 
 
 + 21 
 
 74 
 
 107 
 
 + 33 
 
 42 
 
 10929 
 
 ' 444 
 
 432 
 
 - 12 
 
 109 
 
 103 
 
 - 6 
 
 43 
 
 10340 
 
 335 
 
 329 
 
 - 6 
 
 104 
 
 99 
 
 - 5 
 
 44 
 
 16070 
 
 231 
 
 230 
 
 - 1 
 
 161 
 
 96 
 
 - 65 
 
 45 
 
 7012 
 
 70 
 
 134 
 
 + 64 
 
 70 
 
 93 
 
 + 23 
 
 46 
 
 967 
 
 
 
 
 
 
 
 47 
 
 712 
 
 
 
 
 
 
 
 4S 
 
 699 
 
 
 
 
 
 
 
 49 
 
 469 
 
 
 
 
 
 
 
 50 & 
 
 2366 
 
 
 
 
 
 
 1 
 
 over. 
 
 
 
 
 
 
 
 1 
 
10 AGES OF VOLUNTEERS. 
 
 The trustworthiness of the equations from which the " calcu- 
 lated " numbers in this table are derived will be readily esti- 
 mated upon inspection of the two columns which exhibit the 
 difference between the calculated and observed numbers at the 
 different years of age ; and the substitution of the numerical 
 values of the constants in equations (6) and (7) enables us to 
 determine without difficulty the actual average age which corre- 
 sponds to any given " age last birthday." 
 
 Making these numerical substitutions, the equations assume the 
 form 
 
 — n + 102.507 (0.85362)" = — 27.2949 -f 0.01298027 s n (8) 
 
 t — 102.507 (0.85362)' = — 27.2949 -f 0.01298027 s n+i (9) 
 
 and yield at once the true ages corresponding to the average of 
 the ages " at last birthday," which will be found as follows : — 
 
 Age last 
 birthday. 
 
 18 
 
 Corresponding 
 average age. 
 
 18.4814 
 
 23 
 
 23.4826 
 
 28 
 
 28.4843 
 
 33 
 
 33.4885 
 
 38 
 
 38.4924 
 
 43 
 
 43.4956 
 
 45 
 
 45.4968 
 
 Intermediate values may be found by interpolation with all need- 
 ful accuracy. 
 
 Tables similar to Table II. prepared for each arm of the services 
 independently, and for nine States or groups of States, and num- 
 bered as Tables III. to XIY. inclusive, are appended. 
 
 Such tables were originally constructed for a much larger num- 
 ber of groups ; but these twelve will abundantly suffice to make 
 manifest all the marked phenomena which the more detailed 
 series has brought to light. 
 
AGES OF VOLUNTEERS. 
 
 TABLE III. 
 
 United States Volunteer Infantry. 
 
 11 
 
 Age 
 
 at last 
 
 birthday. 
 
 Number 
 
 at each year 
 
 of age. 
 
 Proportion 
 epecifi 
 
 Observed. 
 
 at and over 
 ed age. 
 
 Calculated. 
 
 Difference. 
 (C. - O.) 
 
 Proportion 
 of a 
 
 Observed. 
 
 it each year 
 
 ge. 
 
 Calculated. 
 
 Difference. 
 (0.-O.) 
 
 13 
 
 113 
 
 
 
 
 
 
 
 14 
 
 288 
 
 
 
 
 
 
 
 15 
 
 636 
 
 
 
 
 
 
 
 16 
 
 2053 
 
 
 
 
 
 
 
 17 
 
 4653 
 
 
 
 
 
 
 
 18 
 
 103420 
 
 10000 
 
 10000 
 
 
 
 1337 
 
 1252 
 
 - 85 
 
 19 
 
 71226 
 
 8663 
 
 8748 
 
 + 85 
 
 921 
 
 1078 
 
 +157 
 
 20 
 
 56238 
 
 7742 
 
 7670 
 
 - 72 
 
 727 
 
 921 
 
 +194 
 
 21 
 
 75978 
 
 7015 
 
 6749 
 
 -266 
 
 983 
 
 802 
 
 -181 
 
 22 
 
 57485 
 
 6032 
 
 5947 
 
 - 85 
 
 743 
 
 69.4 
 
 - 49 
 
 23 
 
 48954 
 
 5289 
 
 5253 
 
 - 36 
 
 633 
 
 602 
 
 - 31 
 
 24 
 
 40852 
 
 4656 
 
 4651 
 
 - 5 
 
 528 
 
 524 
 
 - 4 
 
 25 
 
 36383 
 
 4128 
 
 4127 
 
 - 1 
 
 470 
 
 458 
 
 - 12 
 
 26 
 
 31292 
 
 3658 
 
 3669 
 
 + 11 
 
 405 
 
 401 
 
 - 4 
 
 27 
 
 26369 
 
 3253 
 
 3268 
 
 + 15 
 
 341 
 
 353 
 
 + 12 
 
 28 
 
 27196 
 
 2912 
 
 2915 
 
 + 3 
 
 352 
 
 312 
 
 - 40 
 
 29 . 
 
 18833 
 
 2560 
 
 2603 
 
 .+ 43 
 
 244 
 
 276 
 
 + 32 
 
 30 
 
 21937 
 
 2316 
 
 2327 
 
 + 11 
 
 284 
 
 247 
 
 - 37 
 
 31 
 
 12814 
 
 2032 
 
 2080 
 
 + 48 
 
 166 
 
 221 
 
 + 55 
 
 32 
 
 17038 
 
 1866 
 
 1859 
 
 - 7 
 
 220 
 
 200 
 
 - 20 
 
 33 
 
 13678 
 
 1646 
 
 1659 
 
 + 13 
 
 177 
 
 181 
 
 + 4 
 
 34 
 
 12004 
 
 1469 
 
 1478 
 
 + 9 
 
 155 
 
 166 
 
 + 11 
 
 35 
 
 14558 
 
 1314 
 
 1312 
 
 - 2 
 
 188 
 
 152 
 
 - 36 
 
 36 
 
 10437 
 
 1126 
 
 1160 
 
 + 34 
 
 135 
 
 141 
 
 + 6 
 
 37 
 
 8782 
 
 991 
 
 1019 
 
 + 28 
 
 114 
 
 131 
 
 + 17 
 
 38 
 
 10025 
 
 877 
 
 888 
 
 + 11 
 
 130 
 
 123 
 
 - 7 
 
 39 
 
 7200 
 
 747 
 
 765 
 
 + 18 
 
 93 
 
 116 
 
 + 23 
 
 40 
 
 10886 
 
 654 
 
 649 
 
 - 5 
 
 141 
 
 110 
 
 - 31 
 
 41 
 
 5634 
 
 513 
 
 539 
 
 + 26 
 
 73 
 
 105 
 
 + 32 
 
 42 
 
 8369 
 
 440 
 
 434 
 
 - 6 
 
 108 
 
 101 
 
 - 7 
 
 43 
 
 7900 
 
 332 
 
 333 
 
 + 1 
 
 102 
 
 97 
 
 - 5 
 
 44 
 
 12274 
 
 230 
 
 236 
 
 + 6 
 
 159 
 
 94 
 
 - 65 
 
 45 
 
 5509 
 
 71 
 
 142 
 
 + 71 
 
 71 
 
 91 
 
 + 20 
 
 46 
 
 737 
 
 
 
 
 
 
 
 47 
 
 541 
 
 
 
 
 
 
 
 48 
 
 532 
 
 
 
 
 
 
 
 49 
 
 354 
 
 
 
 
 
 
 
 50 
 
 1942 
 
 
 
 
 
 
 1 
 
12 
 
 AGES OF VOLUNTEERS. 
 
 TABLE IV. 
 
 United States Volunteer Cavalry. 
 
 Age 
 1 at last 
 birthday. 
 
 Number. 
 
 at each year 
 
 of age. 
 
 Proportion 
 specifi 
 
 Observed. 
 
 at and over 
 ed age. 
 
 Calculated. 
 
 Difference. 
 (C. - O.) 
 
 Proportion t 
 of a 
 
 Observed. 
 
 it each year 
 Calculated. 
 
 Difference. 
 (C. - O.) 
 
 13 
 
 5 
 
 
 
 
 
 
 
 1 U 
 
 15 
 
 
 
 
 
 
 
 15 
 
 49 
 
 
 
 
 
 
 
 16 
 
 232 
 
 
 
 
 
 
 
 17 
 
 638 
 
 
 
 
 
 
 
 18 
 
 15013 
 
 10000 
 
 10000 
 
 
 
 1295 
 
 1240 
 
 - 55 
 
 19 
 
 9767 
 
 8705 
 
 8760 
 
 + 55 
 
 842 
 
 1074 
 
 +232 
 
 20 
 
 7864 
 
 7863 
 
 7686 
 
 -177 
 
 682 
 
 931 
 
 +249 
 
 21 
 
 12081 
 
 7181 
 
 6755 
 
 -426 
 
 1042 
 
 808 
 
 -234 
 
 22 
 
 90.96 
 
 6139 
 
 5947 
 
 -192 
 
 784 
 
 703 
 
 - 81 
 
 23 
 
 7806 
 
 5355 
 
 5244 
 
 -111 
 
 673 
 
 612 
 
 - 61 
 
 24 
 
 6361 
 
 4682 
 
 4632 
 
 - 50 
 
 549 
 
 534 
 
 - 15 
 
 25 
 
 5724 
 
 4133 
 
 4098 
 
 - 35 
 
 494 
 
 467 
 
 - 27 
 
 1 26 
 
 4831 
 
 3639 
 
 3631 
 
 - 8 
 
 417 
 
 410 
 
 - 7 
 
 27 
 
 4192 
 
 3222 
 
 3221 
 
 - 1 
 
 360 
 
 360 
 
 
 
 28 
 
 4318 
 
 2862 
 
 2861 
 
 - 1 
 
 372 
 
 318 
 
 - 54 
 
 29 
 
 2845 
 
 2490 
 
 2543 
 
 + 53 
 
 245 
 
 281 
 
 + v 36 
 
 30 
 
 3251 
 
 2245 
 
 2262 
 
 + 17 
 
 280 
 
 250 
 
 - 30 
 
 31 
 
 2043 
 
 1965 
 
 2012 
 
 + 47 
 
 176 
 
 223 
 
 + 47 
 
 32 
 
 2450 
 
 1789 
 
 1789 
 
 
 
 211 
 
 200 
 
 - 11 
 
 1 33 
 
 1950 
 
 1578 
 
 1589 
 
 + 11 
 
 168 
 
 180 
 
 + 12 
 
 34 
 
 1679 
 
 1410 
 
 1410 
 
 
 
 145 
 
 163 
 
 + 18 
 
 ' 35 
 
 2130 
 
 1265 
 
 1247 
 
 - 18 
 
 184 
 
 148 
 
 - 36 
 
 ! 36 
 
 1541 
 
 10S1 
 
 1098 
 
 + 17 
 
 133 
 
 135 
 
 + 2 
 
 37 
 
 1268 
 
 948 
 
 963 
 
 + 15 
 
 109 
 
 124 
 
 + 15 
 
 38 
 
 1416 
 
 839 
 
 839 
 
 
 
 122 
 
 115 
 
 - 7 
 
 | 39 
 
 979 
 
 717 
 
 724 
 
 + 7 
 
 84 
 
 107 
 
 + 23 
 
 40 
 
 1441 
 
 633 
 
 618 
 
 - 15 
 
 124 
 
 100 
 
 - 24 
 
 41 
 
 822 
 
 509 
 
 518 
 
 + 8 
 
 71 
 
 94 
 
 + 23 
 
 42 
 
 1199 
 
 438 
 
 426 
 
 - 12 
 
 103 
 
 89 
 
 - 14 
 
 43 
 
 1079 
 
 335 
 
 337 
 
 + 2 
 
 93 
 
 85 
 
 - 8 
 
 44 
 
 1851 
 
 242 
 
 252 
 
 + 10 
 
 160 
 
 81 
 
 -79 
 
 45 
 
 954 
 
 82 
 
 170 
 
 + 88 
 
 82 
 
 78 
 
 - 4 
 
 46 
 
 105 
 
 
 
 
 
 
 
 47 
 
 74 
 
 
 
 
 
 
 
 ! 48 
 
 73 
 
 
 
 
 
 
 
 i 49 
 
 60 
 
 
 
 
 
 
 
 50 
 
 1 
 
 203 
 
 
 
 
 
 
 
AGES OF VOLUNTEERS. 
 
 TABLE V . 
 
 United States Volunteer Artillery. 
 
 13 
 
 Age 
 
 at last 
 
 birthday. 
 
 Number 
 
 at eacb. year 
 
 of age. 
 
 Proportion 
 specifi 
 
 Observed. 
 
 at and over 
 ;d age. 
 
 Calculated. 
 
 Difference. 
 (C. - O.) 
 
 Proportion i 
 of a 
 
 Observed. 
 
 it each year 
 ge. 
 
 Calculated. 
 
 Difference. 
 (C.-O.) 
 
 14 
 
 2 
 
 
 
 
 
 
 
 15 
 
 21 
 
 
 
 
 
 
 
 16 
 
 61 
 
 
 
 
 
 
 
 17 
 
 226 
 
 
 
 
 
 
 
 18 
 
 5400 
 
 10000 
 
 10000 
 
 
 
 1275 
 
 1179 
 
 - 96 
 
 19 
 
 3439 
 
 8725 
 
 8821 
 
 + 96 
 
 812 
 
 1024 
 
 4212 
 
 20 
 
 2627 
 
 7913 
 
 7797 
 
 -116 
 
 620 
 
 891 
 
 +271 
 
 21 
 
 4416 
 
 7293 
 
 6906 
 
 -387 
 
 1042 
 
 776 
 
 -266 
 
 22 
 
 3107 
 
 6251 
 
 6130 
 
 -121 
 
 • 734 
 
 678 
 
 - 56 
 
 23 
 
 2759 
 
 5517 
 
 5452 
 
 - 65 
 
 651 
 
 593 
 
 - 58 
 
 24 
 
 2163 
 
 4866 
 
 4859 
 
 - 7 
 
 511 
 
 521 
 
 + 10 
 
 25 
 
 2012 
 
 4355 
 
 4338 
 
 - 17 
 
 475 
 
 459 
 
 - 16 
 
 26 
 
 1768 
 
 3880 
 
 3879 
 
 - 1 
 
 417 
 
 405 
 
 - 12 
 
 27 
 
 1505 
 
 3463 
 
 3474 
 
 + 11 
 
 355 
 
 359 
 
 + 4 
 
 28 
 
 1525 
 
 3108 
 
 3115 
 
 + 7 
 
 360 
 
 320 
 
 - 40 
 
 29 
 
 1087 
 
 2748 
 
 2795 
 
 + 47 
 
 257 
 
 286 
 
 + 29 
 
 30 
 
 1213 
 
 2491 
 
 2509 
 
 + 18 
 
 286 
 
 257 
 
 - 29 
 
 31 
 
 796 
 
 2205 
 
 2252 
 
 + 47 
 
 188 
 
 232 
 
 + 44 
 
 32 
 
 931 
 
 2017 
 
 2020 
 
 + 3 
 
 220 
 
 211 
 
 - 9 
 
 33 
 
 753 
 
 1797 
 
 1809 
 
 + 12 
 
 178 
 
 193 
 
 + 15 
 
 34 
 
 724 
 
 1619 
 
 1616 
 
 - 3 
 
 171 
 
 177 
 
 + 6 
 
 35 
 
 836 
 
 1448 
 
 1439 
 
 - 9 
 
 197 
 
 163 
 
 - 34 
 
 36 
 
 702 
 
 1251 
 
 1276 
 
 + 25 
 
 166 
 
 151 
 
 - 15 
 
 37 
 
 477 
 
 1085 
 
 1125 
 
 + 40 
 
 113 
 
 142 
 
 + 29 
 
 38 
 
 579 
 
 972 
 
 983 
 
 + 11 
 
 137 
 
 133 
 
 - 4 
 
 39 
 
 416 
 
 835 
 
 850 
 
 + 15 
 
 98 
 
 126 
 
 + 28 
 
 40 
 
 649 
 
 737 
 
 724 
 
 - 13 
 
 153 
 
 119 
 
 - 34 
 
 41 
 
 320 
 
 584 
 
 605 
 
 + 21 
 
 76 
 
 114 
 
 + 38 
 
 42 
 
 535 
 
 508 
 
 491 
 
 - 17 
 
 126 
 
 109 
 
 - 17 
 
 43 
 
 533 
 
 382 
 
 382 
 
 
 
 126 
 
 105 
 
 - 21 
 
 44 
 
 796 
 
 256 
 
 277 
 
 + 21 
 
 188 
 
 102 
 
 - 86 
 
 45 
 
 289 
 
 68 
 
 175 
 
 +107 
 
 68 
 
 100 
 
 + 32 
 
 46 
 
 45 
 
 
 
 
 
 
 
 47 
 
 34 
 
 
 
 
 
 
 
 48 
 
 31 
 
 
 
 
 
 
 
 49 
 
 17 
 
 
 
 
 
 
 
 50 
 
 68 
 
 
 
 
 
 
 
14 AGES OF VOLUNTEERS. 
 
 TABLE VI. 
 
 Ages of Maine, New Hampshire, Vermont, and Connecticut VoVs. 
 
 Age 
 
 at last 
 
 birthday. 
 
 Number. 
 
 at each year 
 
 of age. 
 
 Proportion 
 specifi 
 
 Observed. 
 
 at and over 
 ed age. 
 
 Calculated. 
 
 Difference. 
 (C. - O.) 
 
 Proportion 
 of a 
 
 Observed. 
 
 it each year 
 Calculated. 
 
 Difference. 
 (C. - O.) 
 
 13 
 
 3 
 
 
 
 
 
 
 
 14 
 
 10 
 
 
 
 
 
 
 
 15 
 
 27 
 
 
 
 
 
 
 
 16 
 
 95 
 
 
 
 
 
 
 
 17 
 
 223 
 
 
 
 
 
 
 
 18 
 
 11694 
 
 10000 
 
 10001 
 
 + 1 
 
 1522 
 
 1245 
 
 -277 
 
 19 
 
 6541 
 
 8478 
 
 8756 
 
 +278 
 
 852 
 
 1071 
 
 4219 
 
 20 
 
 5311 
 
 7626 
 
 7685 
 
 + 59 
 
 691 
 
 923 
 
 +232 
 
 21 
 
 7477 
 
 6935 
 
 6762 
 
 -173 
 
 976 
 
 800 
 
 -176 
 
 22 
 
 5356 
 
 5959 
 
 5962 
 
 + 3 
 
 699 
 
 685 
 
 - 14 
 
 23 
 
 4614 
 
 5260 
 
 5277 
 
 + 17 
 
 604 
 
 598 
 
 - 6 
 
 24 
 
 3824 
 
 4656 
 
 4679 
 
 + 23 
 
 500 
 
 519 
 
 + 19 
 
 25 
 
 3357 
 
 4156 
 
 4160 
 
 + 4 
 
 440 
 
 453 
 
 + 13 
 
 26 
 
 2988 
 
 3716 
 
 3707 
 
 - 9 
 
 390 
 
 397 
 
 + 7 
 
 27 
 
 2590 
 
 3326 
 
 3310 
 
 - 16 
 
 338 
 
 350 
 
 + 12 
 
 28 
 
 2762 
 
 2988 
 
 2960 
 
 - 28 
 
 361 
 
 307 
 
 - 54 
 
 29 
 
 1881 
 
 2627 
 
 2653 
 
 + 26 
 
 245 
 
 273 
 
 + 28 
 
 30 
 
 1983 
 
 2382 
 
 2380 
 
 - 2 
 
 259 
 
 243 
 
 - 16 
 
 31 
 
 1362 
 
 2123 
 
 2137 
 
 + 14 
 
 177 
 
 218 
 
 + 41 
 
 32 
 
 1609 
 
 1946 
 
 1919 
 
 - 27 
 
 210 
 
 196 
 
 - 14 
 
 33 
 
 1427 
 
 1736 
 
 1723 
 
 - 13 
 
 185 
 
 178 
 
 - 7 
 
 34 
 
 1141 
 
 1551 
 
 1545 
 
 - 6 
 
 149 
 
 163 
 
 + 14 
 
 35 
 
 1355 
 
 1402 
 
 1382 
 
 - 20 
 
 176 
 
 149 
 
 - 27 
 
 36 
 
 1046 
 
 1226 
 
 1233 
 
 + 7 
 
 136 
 
 138 
 
 + 2 
 
 37 
 
 989 
 
 1090 
 
 1095 
 
 + 5 
 
 127 
 
 ' 128 
 
 + 1 
 
 38 
 
 1005 
 
 963 
 
 967 
 
 + 4 
 
 131 
 
 118 
 
 - 13 
 
 39 
 
 817 
 
 832 
 
 849 
 
 + 17 
 
 107 
 
 115 
 
 + 8 
 
 40 
 
 969 
 
 725 
 
 734 
 
 + 9 
 
 127 
 
 108 
 
 - 19 
 
 41 
 
 604 
 
 598 
 
 626 
 
 + 28 
 
 77 
 
 102 
 
 + 25 
 
 42 
 
 882 
 
 521 
 
 524 
 
 + 3 
 
 115 
 
 97 
 
 - 18 
 
 43 
 
 870 
 
 406 
 
 427 
 
 + 21 
 
 113 
 
 95 
 
 - 18 
 
 44 
 
 1789 
 
 293 
 
 332 
 
 + 39 
 
 233 
 
 90 
 
 -143 
 
 45 
 
 459 
 
 60 
 
 242 
 
 +182 
 
 60 
 
 88 
 
 + 28 
 
 46 
 
 50 
 
 
 
 
 
 
 
 47 
 
 38 
 
 
 
 
 
 
 
 48 
 
 34 
 
 
 
 
 
 
 
 49 
 
 23 
 
 
 
 
 
 
 
 50 & 
 
 60 
 
 
 
 
 
 
 
 over. 
 
 
 
 
 
 
 
 
AGES OF VOLUNTEERS. 
 
 TABLE VII. 
 
 Ages of Massachusetts Volunteers. 
 
 15 
 
 Age 
 
 at last 
 
 birthday. 
 
 Number 
 
 at each year 
 
 of age. 
 
 Proportion 
 specifi 
 
 Observed. 
 
 at and over 
 ed age. 
 
 Calculated. 
 
 Difference. 
 (C. - O.) 
 
 Proportion 
 of a 
 
 Observed. 
 
 it each year 
 ge. 
 
 Calculated. 
 
 Difference. 
 (C.-O.) 
 
 12 
 
 4 
 
 
 
 
 
 
 
 13 
 
 4 
 
 
 
 
 
 
 
 14 
 
 26 
 
 
 
 
 
 
 
 15 
 
 44 
 
 
 
 
 
 
 
 16 
 
 101 
 
 
 
 
 
 
 
 17 
 
 289 
 
 
 
 
 
 
 
 18 
 
 6894 
 
 10000 
 
 10000 
 
 
 
 1269 
 
 1145 
 
 -124 . 
 
 19 
 
 4582 
 
 8731 
 
 8855 
 
 +124 
 
 846 
 
 1002 
 
 +156 
 
 20 
 
 3604 
 
 7885 
 
 7853 
 
 - 32 
 
 666 
 
 877 
 
 +211 
 
 21 
 
 5429 
 
 7219 
 
 6976 
 
 -243 
 
 1003 
 
 771 
 
 -232 
 
 22 
 
 3860 
 
 6216 
 
 6205 
 
 - 11 
 
 713 
 
 678 
 
 - 35 
 
 23 
 
 3203 
 
 5513 
 
 5527 
 
 + 14 
 
 592 
 
 597 
 
 + 5 
 
 24 
 
 2871 
 
 4921 
 
 4930 
 
 + 9 
 
 530 
 
 528 
 
 - 2 
 
 25 
 
 2474 
 
 4391 
 
 4402 
 
 + 11 
 
 457 
 
 467 
 
 + 10 
 
 26 
 
 2232 
 
 3934 
 
 3935 
 
 + 1 
 
 412 
 
 415 
 
 + 3 
 
 27 
 
 1962 
 
 3522 
 
 3520 
 
 - 2 
 
 362 
 
 370 
 
 + 8 
 
 28 
 
 2041 
 
 3160 
 
 3150 
 
 - 10 
 
 377 
 
 330 
 
 - 47 
 
 29 
 
 1411 
 
 2783 
 
 2820 
 
 + 37 
 
 260 
 
 296 
 
 + 36 
 
 30 
 
 1564 
 
 2523 
 
 2524 
 
 + 1 
 
 288 
 
 267 
 
 - 21 
 
 31 
 
 988 
 
 2235 
 
 2257 
 
 + 22 
 
 183 
 
 242 
 
 + 59 
 
 32 
 
 1233 
 
 2042 
 
 2015 
 
 - 27 
 
 228 
 
 219 
 
 - 9 
 
 33 
 
 1041 
 
 1814 
 
 1796 
 
 - 18 
 
 193 
 
 200 
 
 + 7 
 
 34 
 
 980 
 
 1621 
 
 1596 
 
 - 25 
 
 181 
 
 184 
 
 + 3 
 
 35 
 
 1213 
 
 1440 
 
 1412 
 
 - 28 
 
 224 
 
 169 
 
 - 55 
 
 36 
 
 761 
 
 1216 
 
 1243 
 
 + 27 
 
 141 
 
 157 
 
 + 16 
 
 37 
 
 699 
 
 1075 
 
 1086 
 
 + 11 
 
 129 
 
 146 
 
 + 17 
 
 38 
 
 828 
 
 946 
 
 940 
 
 - 6 
 
 153 
 
 137 
 
 - 16 
 
 39 
 
 600 
 
 793 
 
 803 
 
 + 10 
 
 111 
 
 129 
 
 + 18 
 
 40 
 
 838 
 
 682 
 
 674 
 
 - 8 
 
 155 
 
 122 
 
 - 33 
 
 41 
 
 440 
 
 527 
 
 552 
 
 + 25 
 
 81 
 
 116 
 
 + 35 
 
 42 
 
 658 
 
 446 
 
 436 
 
 - 10 
 
 122 
 
 110 
 
 - 12 
 
 43 
 
 596 
 
 324 
 
 326 
 
 + 2 
 
 110 
 
 106 
 
 - 4 
 
 44 
 
 859 
 
 214 
 
 220 
 
 + 6 
 
 159 
 
 102 
 
 - 57 
 
 45 
 
 296 
 
 55 
 
 118 
 
 + 63 
 
 55 
 
 98 
 
 + 43 
 
 46 
 
 28 
 
 
 
 
 
 
 
 47 
 
 14 
 
 
 
 
 
 
 
 48 
 
 16 
 
 
 
 
 
 
 
 49 
 
 9 
 
 
 
 
 
 
 
 50 & 
 
 33 
 
 
 
 
 
 
 
 over. 
 
 
 
 
 
 
 
 
16 
 
 AGES OF VOLUNTEERS. 
 
 TABLE VIII. 
 
 Ages of New York Volunteers. 
 
 J 
 
 Age 
 
 at last 
 
 birthday. 
 
 Number. 
 
 at each year 
 
 of age. 
 
 Proportion 
 specifi 
 
 Observed. 
 
 it and over 
 3d age. 
 
 Calculated. 
 
 Difference. 
 (C.-O.) 
 
 Proportion a 
 of a{ 
 
 Observed. 
 
 t each year 
 Calculated. 
 
 Difference. 
 (C.-O.) 
 
 13 
 
 17 
 
 
 
 
 • 
 
 
 
 14 
 
 63 
 
 
 
 
 
 
 
 15 
 
 153 
 
 
 
 
 
 
 
 16 
 
 448 
 
 
 
 
 
 
 
 17 
 
 699 
 
 
 
 
 
 
 
 . 18 
 
 19737 
 
 10000 
 
 10000 
 
 
 
 1087 
 
 1173 
 
 + 86 
 
 19 
 
 16233 
 
 8913 
 
 8827 
 
 - 86 
 
 894 
 
 1019 
 
 +125 
 
 20 
 
 11286 
 
 8019 
 
 7808 
 
 -211 
 
 621 
 
 887 
 
 +266 
 
 21 
 
 20227 
 
 7398 
 
 6922 
 
 -476 
 
 1114 
 
 773 
 
 -341 
 
 22 
 
 13689 
 
 6284 
 
 6149 
 
 -135 
 
 754 
 
 675 
 
 - 79 
 
 23 
 
 11516 
 
 5530 
 
 5774 
 
 +244 
 
 634 
 
 592 
 
 - 42 
 
 24 
 
 9488 
 
 4896 
 
 4882 
 
 - 14 
 
 523 
 
 520 
 
 - 3 
 
 25 
 
 8648 
 
 4373 
 
 4363 
 
 - 10 
 
 476 
 
 459 
 
 - 17 
 
 26 
 
 7285 
 
 3897 
 
 3904 
 
 + 7 
 
 401 
 
 406 
 
 + 5 
 
 27 
 
 6223 
 
 3496 
 
 3498 
 
 + 2 
 
 343 
 
 360 
 
 + 17 
 
 28 
 
 6652 
 
 3153 
 
 3138 
 
 - 15 
 
 366 
 
 322 
 
 - 44 
 
 29 
 
 4552 
 
 2787 
 
 2816 
 
 + 29 
 
 251 
 
 289 
 
 + 38 
 
 30 
 
 5474 
 
 2536 
 
 2527 
 
 - 9 
 
 301 
 
 260 
 
 - 41 
 
 31 
 
 3287 
 
 2235 
 
 2267 
 
 + 32 
 
 181 
 
 236 
 
 + 55 
 
 32, 
 
 4533 
 
 2054 
 
 2031 
 
 - 23 
 
 249 
 
 215 
 
 - 34 
 
 33 
 
 3330 
 
 1805 
 
 1816 
 
 + 11 
 
 184 
 
 197 
 
 + 13 
 
 34 
 
 3135 
 
 1621 
 
 1619 
 
 - 2 
 
 173 
 
 182 
 
 + 9 
 
 35 
 
 3885 
 
 1448 
 
 1437 
 
 - 11 
 
 114 
 
 168 
 
 + 54 
 
 36 
 
 2S72 
 
 1234 
 
 1269 
 
 + 35 
 
 158 
 
 157 
 
 - 1 
 
 37 
 
 2201 
 
 1076 
 
 1112 
 
 + 36 
 
 121 
 
 146 
 
 + 25 
 
 38 
 
 2709 
 
 955 
 
 966 
 
 + 11 
 
 149 
 
 139 
 
 - 10 
 
 39 
 
 1858 
 
 806 
 
 827 
 
 + 21 
 
 103 
 
 132 
 
 + 29 
 
 40 
 
 3157 
 
 703 
 
 695 
 
 - 8 
 
 173 
 
 126 
 
 - 47 
 
 41 
 
 1268 
 
 530 
 
 569 
 
 + 39 
 
 70 
 
 121 
 
 + 51 
 
 42 
 
 2302 
 
 460 
 
 448 
 
 - 12 
 
 127 
 
 116 
 
 - 11 
 
 43 
 
 2068 
 
 333 
 
 332 
 
 - 1 
 
 114 
 
 112 
 
 - 2 
 
 44 
 
 3148 
 
 219 
 
 220 
 
 + 1 
 
 173 
 
 109 
 
 - 64 
 
 45 
 
 831 
 
 46 
 
 111 
 
 + 65 
 
 46 
 
 106 
 
 + 60 
 
 46 
 
 87 
 
 
 
 
 
 
 
 47 
 
 41 
 
 
 
 
 
 
 
 48 
 
 53 
 
 
 
 
 
 
 
 49 
 
 23 
 
 
 
 
 
 
 
 50 & 
 
 103 
 
 
 
 
 
 
 
 over. 
 
 
 
 
 
 
 * — 
 
 
AGES OF VOLUNTEERS. 
 
 TABLE IX. 
 
 Ages of Pennsylvania Volunteers (including Reserves). 
 
 17 
 
 Age 
 
 at last 
 
 birthday. 
 
 Number 
 
 at each year 
 
 of age. 
 
 Proportion 
 specifi 
 
 Observed. 
 
 at and over 
 ed age. 
 
 Calculated. 
 
 Difference. 
 (C. - O.) 
 
 Proportion at each year 
 of age. 
 
 Observed. Calculated. 
 
 Difference. 
 (C.-O.) 
 
 13 
 
 23 
 
 
 • 
 
 
 
 
 
 14 
 
 51 
 
 
 
 
 
 
 
 15 
 
 85 
 
 
 
 
 
 
 
 16 
 
 241 
 
 
 
 
 
 
 
 17 
 
 486 
 
 
 
 
 
 
 
 18 
 
 13052 
 
 10000 
 
 10000 
 
 
 
 1137 
 
 1339 
 
 +202 
 
 19 
 
 11410 
 
 8863 
 
 8661 
 
 -202 
 
 994 
 
 1131 
 
 + 137 
 
 20 
 
 8234 
 
 7869 
 
 7530 
 
 -339 
 
 717 
 
 959 
 
 +242 
 
 21 
 
 13336 
 
 7152 
 
 6571 
 
 -581 
 
 1161 
 
 814 
 
 -347 
 
 22 
 
 9376 
 
 5991 
 
 5757 
 
 -234 
 
 816 
 
 694 
 
 -122 
 
 23 
 
 7696 
 
 5175 
 
 5063 
 
 -112 
 
 670 
 
 595 
 
 - 75 
 
 24 
 
 6061 
 
 4505 
 
 4468 
 
 - 37 
 
 528 
 
 510 
 
 - 18 
 
 25 
 
 5375 
 
 3977 
 
 3958 
 
 - 19 
 
 468 
 
 441 
 
 - 27 
 
 26 
 
 4420 
 
 3509 
 
 3517 
 
 + 8 
 
 385 
 
 382 
 
 - 3 
 
 27 
 
 3576 
 
 3124 
 
 3135 
 
 + 11 
 
 311 
 
 334 
 
 + 23 
 
 28 
 
 3817 
 
 2813 
 
 2801 
 
 - 12 
 
 332 
 
 293 
 
 - 39 
 
 29 
 
 2644 
 
 2481 
 
 2508 
 
 + 27 
 
 230 
 
 260 
 
 + 30 
 
 30 
 
 2926 
 
 2251 
 
 2248 
 
 - 3 
 
 255 
 
 232 
 
 - 23 
 
 31 
 
 2029 
 
 1996 
 
 2016 
 
 + 20 
 
 177 
 
 208 
 
 + 31 
 
 32 
 
 2375 
 
 1819 
 
 1808 
 
 - 11 
 
 207 
 
 188 
 
 - 19 
 
 33 
 
 1903 
 
 1612 
 
 1620 
 
 + 8 
 
 166 
 
 173 
 
 + 7 
 
 34 
 
 1657 
 
 1446 
 
 1447 
 
 + 1 
 
 144 
 
 158 
 
 + 14 
 
 35 
 
 2089 
 
 1302 
 
 1289 
 
 - 13 
 
 182 
 
 147 
 
 - 35 
 
 36 
 
 1490 
 
 1120 
 
 1142 
 
 + 22 
 
 13« 
 
 138 
 
 + 8 
 
 37 
 
 1290 
 
 990 
 
 1004 
 
 + 14 
 
 112 
 
 130 
 
 + 18 
 
 38 
 
 1434 
 
 878 
 
 874 
 
 - 4 
 
 125 
 
 124 
 
 - 1 
 
 39 
 
 1141 
 
 753 
 
 750 
 
 - 3 
 
 99 
 
 118 
 
 + 19 
 
 40 
 
 1692 
 
 654 
 
 632 
 
 - 22 
 
 147 
 
 113 
 
 - 34 
 
 41 
 
 918 
 
 507 
 
 519 
 
 + 12 
 
 80 
 
 109 
 
 + 29 
 
 42 
 
 1431 
 
 427 
 
 410 
 
 + 17 
 
 124 
 
 106 
 
 - 18 
 
 43 
 
 1318 
 
 303 
 
 307 
 
 + 4 
 
 115 
 
 103 
 
 - 12 
 
 44 
 
 1674 
 
 188 
 
 206 
 
 + IS 
 
 146 
 
 101 
 
 - 45 
 
 45 
 
 480 
 
 42 
 
 105 
 
 + 63 
 
 42 
 
 99 
 
 + 57 
 
 46 
 
 73 
 
 
 
 
 
 
 
 47 
 
 46 
 
 
 
 
 
 
 
 48 
 
 49 
 
 
 
 
 
 
 
 49 
 
 36 
 
 
 
 
 
 
 
 50 & 
 
 109 
 
 
 
 
 
 
 
 over. 
 
 
 
 
 
 
 
 ■ — ' 
 
18 
 
 AGES OF VOLUNTEERS. 
 
 TABLE X. 
 
 Ages of Ohio Volunteers. 
 
 Age 
 
 at last 
 
 birthday. 
 
 Number 
 
 at each year 
 
 of age. 
 
 Proportion 
 specif! 
 
 Observed. 
 
 it and over 
 jd age. 
 
 Calculated. 
 
 Difference. 
 (C. - O.) 
 
 Proportion a 
 of ag 
 
 Observed. 
 
 t each year 
 re- 
 calculated. 
 
 Difference. 
 (C. - O.) 
 
 13 
 
 21 
 
 
 * 
 
 
 
 
 
 14 
 
 44 
 
 
 
 
 
 
 
 15 
 
 103 
 
 
 
 
 
 
 
 16 
 
 470 
 
 
 
 
 
 
 
 17 
 
 1476 
 
 
 
 
 
 
 
 18 
 
 23495 
 
 10000 
 
 10000 
 
 
 
 1567 
 
 1359 
 
 -208 
 
 19 
 
 14986 
 
 8433 
 
 8641 
 
 +208 
 
 999 
 
 1143 
 
 +144 
 
 20 
 
 12358 
 
 7434 
 
 7498 
 
 + 64 
 
 825 
 
 963 
 
 + 138 
 
 21 
 
 12819 
 
 6609 
 
 6535 
 
 - 74 
 
 855 
 
 815 
 
 - 40 
 
 22 
 
 10499 
 
 5754 
 
 5720 
 
 - 34 
 
 700 
 
 692 
 
 - 8 
 
 23 
 
 9297 
 
 5054 
 
 5028 
 
 - 26 
 
 620 
 
 590 
 
 - 30 
 
 24 
 
 7327 
 
 4434 
 
 4438 
 
 - 6 
 
 489 
 
 505 
 
 + 16 
 
 25 
 
 6502 
 
 3945 
 
 3933 
 
 - 12 
 
 430 
 
 435 
 
 + 5 
 
 26 
 
 5678 
 
 3515 
 
 3498 
 
 - 17 
 
 382 
 
 377 
 
 - 5 
 
 27 
 
 4739 
 
 3133 
 
 3121 
 
 - 12 
 
 316 
 
 329 
 
 + 13 
 
 28 
 
 4997 
 
 2817 
 
 2792 
 
 - 25 
 
 333 
 
 289 
 
 - 44 
 
 29 
 
 3570 
 
 2484 
 
 2503 
 
 + 19 
 
 238 
 
 256 
 
 + 18 
 
 30 
 
 3960 
 
 2246 
 
 2247 
 
 + 1 
 
 264 
 
 228 
 
 - 36 
 
 31 
 
 2596 
 
 1982 
 
 2019 
 
 + 37 
 
 174 
 
 206 
 
 + 32 
 
 32 
 
 3029 
 
 1808 
 
 1813 
 
 + 5 
 
 201 
 
 187 
 
 - 14 
 
 33 
 
 2669 
 
 1607 
 
 1626 
 
 + 19 
 
 178 
 
 171 
 
 - 7 
 
 34 
 
 2302 
 
 1429 
 
 1455 
 
 + 26 
 
 154 
 
 159 
 
 + 5 
 
 35 
 
 2659 
 
 1275 
 
 1296 
 
 + 21 
 
 178 
 
 148 
 
 - 30 
 
 36 
 
 2216 
 
 • 1097 
 
 1148 
 
 + 51 
 
 147 
 
 139 
 
 - 8 
 
 37 
 
 1830 
 
 950 
 
 1009 
 
 + 59 
 
 123 
 
 132 
 
 + 9 
 
 38 
 
 1959 
 
 827 
 
 877 
 
 + 50. 
 
 130 
 
 125 
 
 - 5 
 
 39 
 
 1424 
 
 697 
 
 752 
 
 + 55 
 
 95 
 
 120 
 
 + 25 
 
 40 
 
 1880 
 
 602 
 
 632 
 
 + 30 
 
 126 
 
 116 
 
 - 10 
 
 41 
 
 1097 
 
 476 
 
 516 
 
 + 40 
 
 73 
 
 113 
 
 + 40 
 
 42 
 
 1513 
 
 403 
 
 403 
 
 
 
 101 
 
 110 
 
 + 9 
 
 43 
 
 1337 
 
 302 
 
 293 
 
 - 9 
 
 89 
 
 108 
 
 + 19 
 
 44 
 
 2070 
 
 213 
 
 185 
 
 - 28 
 
 138 
 
 106 
 
 - 32 
 
 45 
 
 1128 
 
 75 
 
 79 
 
 + 4 
 
 75 
 
 104 
 
 + 29 
 
 46 
 
 202 
 
 
 
 
 
 
 
 47 
 
 161 
 
 
 
 
 
 
 
 48 
 
 145 
 
 
 
 
 
 
 
 49 
 
 104 
 
 
 
 
 
 
 
 50 & 
 
 471 
 
 
 
 
 
 
 
 over. 
 
 
 
 
 
 
 
 1 
 
AGES OF VOLUNTEERS. 
 
 TABLE XI. 
 
 Ages of Indiana Volunteers. 
 
 19 
 
 Age 
 
 at last 
 
 birthday. 
 
 Number 
 
 at each year 
 
 of age. 
 
 Proportion 
 speciti 
 
 Observed. 
 
 at and over 
 ed age. 
 
 Calculated. 
 
 Difference. 
 (C. - O.) 
 
 Proportion < 
 of a 
 
 Observed. 
 
 it each year 
 Be- 
 
 Calculated. 
 
 1 
 Difference. 
 
 (C.-O.) 
 
 13 
 
 13 
 
 
 
 
 
 
 
 14 
 
 16 
 
 
 
 
 
 
 
 15 
 
 39 
 
 
 
 
 
 
 
 16 
 
 162 
 
 
 
 
 
 
 
 17 
 
 578 
 
 
 
 
 
 
 
 18 
 
 11178 
 
 10000 
 
 10000 
 
 
 
 1608 
 
 1446 
 
 -162 
 
 19 
 
 7175 
 
 8392 
 
 8554 
 
 +162 
 
 1032 
 
 1223 
 
 +191 
 
 20 
 
 6478 
 
 7360 
 
 7331 
 
 - 29 
 
 932 
 
 1035 
 
 +103 
 
 21 
 
 6398 
 
 6428 
 
 6296 
 
 -132 
 
 920 
 
 877 
 
 - 43 
 
 22 
 
 5580 
 
 5508 
 
 5419 
 
 - 89 
 
 802 
 
 744 
 
 - 58 
 
 23 
 
 4562 
 
 4706 
 
 4675 
 
 - 31 
 
 656 
 
 632 
 
 -24 
 
 24 
 
 3782 
 
 4050 
 
 4043 
 
 - 7 
 
 544 
 
 538 
 
 - 6 
 
 25 
 
 3216 
 
 3506 
 
 3505 
 
 - 1 
 
 462 
 
 460 
 
 - 2 
 
 26 
 
 2707 
 
 3044 
 
 3045 
 
 + 1 
 
 390 
 
 394 
 
 + 4 
 
 27 
 
 2269 
 
 2654 
 
 2651 
 
 - 3 
 
 326 
 
 337 
 
 + 11 
 
 28 
 
 2272 
 
 2328 
 
 2314 
 
 - 14 
 
 327 
 
 290 
 
 - 37 
 
 29 
 
 1513 
 
 2001 
 
 2024 
 
 + 23 
 
 217 
 
 251 
 
 + 34 
 
 30 
 
 1799 
 
 1784 
 
 1773 
 
 - 11 
 
 259 
 
 218 
 
 - 41 
 
 31 
 
 1013 
 
 1525 
 
 1555 
 
 + 30 
 
 145 
 
 190 
 
 + 45 
 
 32 
 
 1230 
 
 1380 
 
 1365 
 
 - 15 
 
 177 
 
 166 
 
 - 11 
 
 33 
 
 1046 
 
 1203 
 
 1200 
 
 - 3 
 
 151 
 
 146 
 
 - 5 
 
 34 
 
 871 
 
 1052 
 
 1053 
 
 + 1 
 
 125 
 
 130 
 
 + 5 
 
 35 
 
 962 
 
 927 
 
 923 
 
 - 4 
 
 138 
 
 116 
 
 - 22 
 
 36 
 
 666 
 
 789 
 
 806 
 
 + 17 
 
 96 
 
 104 
 
 + 8 
 
 37 
 
 589 
 
 693 
 
 702 
 
 + 9 
 
 85 
 
 94 
 
 + 9 
 
 38 
 
 656 
 
 608 
 
 608 
 
 
 
 94 
 
 86 
 
 - 8 
 
 39 
 
 428 
 
 514 
 
 522 
 
 + 8 
 
 62 
 
 79 
 
 + 17 
 
 40 
 
 683 
 
 452 
 
 443 
 
 - 9 
 
 98 
 
 73 
 
 - 25 
 
 41 
 
 371 
 
 354 
 
 370 
 
 + 16 
 
 53 
 
 68 
 
 + 15 
 
 42 
 
 482 
 
 301 
 
 302 
 
 + 1 
 
 69 
 
 64 
 
 - 5 
 
 43 
 
 471 
 
 232 
 
 238 
 
 + 6 
 
 68 
 
 60 
 
 - 8 
 
 44 
 
 682 
 
 164 
 
 178 
 
 + 14 
 
 98 
 
 57 
 
 - 41 
 
 45 
 
 457 
 
 66 
 
 121 
 
 + 55 
 
 66 
 
 55 
 
 - 11 
 
 46 
 
 70 
 
 
 
 
 
 
 
 47 
 
 37 
 
 
 
 
 
 
 
 48 
 
 50 
 
 
 
 
 
 
 
 49 
 
 24 
 
 
 
 
 
 
 
 50 & 
 
 146 
 
 
 
 
 
 
 
 over. 
 
 
 
 
 
 
 
 I 
 
20 
 
 AGES OF VOLUNTEERS. 
 
 TABLE XII. 
 
 Ages of Michigan Volunteers. 
 
 Age 
 
 at last 
 
 birthday. 
 
 Number. 
 
 at each year 
 
 of age. 
 
 Proportion 
 specifi 
 
 Observed. 
 
 it and over 
 3d age. 
 
 Calculated. 
 
 Difference. 
 (C.-O.) 
 
 Proportion a 
 
 of a 
 
 Observed. 
 
 t each year 
 Calculated. 
 
 Difference. 
 (C. - O.) 
 
 13 
 
 3 
 
 
 
 
 
 
 
 14 
 
 9 
 
 
 
 
 
 
 
 15 
 
 27 
 
 
 
 
 
 
 
 16 
 
 112 
 
 
 
 
 
 
 
 17 
 
 299 
 
 
 
 
 
 
 
 18 
 
 5862 
 
 10000 
 
 10000 
 
 
 
 1523 
 
 1279 
 
 -244 
 
 19 
 
 3437 
 
 8477 
 
 8721 
 
 +244 
 
 893 
 
 1098 
 
 +205 
 
 20 
 
 2767 
 
 7584 
 
 7623 
 
 + 39 
 
 719 
 
 943 
 
 +224 
 
 21 
 
 3727 
 
 6865 
 
 6680 
 
 -185 
 
 968 
 
 812 
 
 -156 
 
 22 
 
 2802 
 
 5897 
 
 5868 
 
 - 29 
 
 728 
 
 700 
 
 - 28 
 
 23 
 
 2337 
 
 5169 
 
 5168 
 
 - 1 
 
 607 
 
 605 
 
 - 2 
 
 24 
 
 1963 
 
 4562 
 
 4563 
 
 + 1 
 
 510 
 
 524 
 
 + 14 
 
 25 
 
 1724 
 
 4052 
 
 4039 
 
 - 13 
 
 448 
 
 455 
 
 + 7 
 
 26 
 
 1568 
 
 3604 
 
 3584 
 
 - 20 
 
 407 
 
 396 
 
 - 11 
 
 27 
 
 1297 
 
 3197 
 
 3188 
 
 - 9 
 
 337 
 
 346 
 
 + 9 
 
 28 
 
 1335 
 
 2860 
 
 2842 
 
 - 18 
 
 347 
 
 304 
 
 - 43 
 
 29 
 
 923 
 
 2513 
 
 2538 
 
 + 25 
 
 240 
 
 268 
 
 + 28 
 
 30 
 
 989 
 
 2273 
 
 2270 
 
 - 3 
 
 257 
 
 237 
 
 - 20 
 
 31 
 
 695 
 
 2016 
 
 2033 
 
 + 17 
 
 180 
 
 211 
 
 + 31 
 
 32 
 
 843 
 
 1836 
 
 1822 
 
 - 14 
 
 219 
 
 188 
 
 - 31 
 
 33 
 
 614 
 
 1617 
 
 1634 
 
 + 17 
 
 160 
 
 169 
 
 + 9 
 
 34 
 
 527 
 
 1457 
 
 1465 
 
 + 8 
 
 137 
 
 153 
 
 + 16 
 
 35 
 
 668 
 
 1320 
 
 1312 
 
 - 8 
 
 173 
 
 140 
 
 - 33 
 
 36 
 
 481 
 
 1147 
 
 1172 
 
 + 25 
 
 125 
 
 128 
 
 + 3 
 
 37 
 
 411 
 
 1022 
 
 1044 
 
 + 22 
 
 107 
 
 118 
 
 + 11 
 
 38 
 
 458 
 
 915 
 
 926 
 
 + 11 
 
 119 
 
 109 
 
 - 10 
 
 39 
 
 313 
 
 796 
 
 817 
 
 + 21 
 
 81 
 
 102 
 
 + 21 
 
 40 
 
 466 
 
 715 
 
 715 
 
 + 
 
 121 
 
 96 
 
 - 25 
 
 41 
 
 256 
 
 594 
 
 619 
 
 + 25 
 
 67 
 
 91 
 
 + 24 
 
 42 
 
 403 
 
 527 
 
 528 
 
 + 1 
 
 105 
 
 86 
 
 - 19 
 
 43 
 
 400 
 
 422 
 
 442 
 
 + 20 
 
 104 
 
 83 
 
 - 21 
 
 44 
 
 825 
 
 318 
 
 359 
 
 + 41 
 
 214 
 
 79 
 
 -135 
 
 45 
 
 398 
 
 104 
 
 280 
 
 +176 
 
 104 
 
 77 
 
 - 27 
 
 46 
 
 44 
 
 
 
 
 
 
 
 47 
 
 23 
 
 
 
 
 
 
 
 48 
 
 26 
 
 
 
 
 
 
 
 49 
 
 14 
 
 
 
 
 
 
 
 50 & 
 
 61 
 
 
 
 
 
 
 
 over. 
 
 
 
 
 
 
 
 
AGES OF VOLUNTEERS. 
 
 TABLE XIII. 
 
 Ages of Illinois Volunteers. 
 
 21 
 
 Age 
 
 at last 
 
 birthday. 
 
 Number 
 
 at each year 
 
 of age. 
 
 Proportion 
 specifi 
 
 Observed. 
 
 at and over 
 ed age. 
 
 Calculated. 
 
 Difference. 
 (C. - O.) 
 
 Proportion i 
 
 of a 
 
 Observed. 
 
 it each year 
 Calculated. 
 
 Difference. 
 (C.-O.) 
 
 13 
 
 5 
 
 
 
 
 
 
 
 14 
 
 23 
 
 
 
 
 
 
 
 15 
 
 65 
 
 
 
 
 
 
 
 16 
 
 250 
 
 
 
 
 
 
 
 17 
 
 539 
 
 
 
 
 
 
 
 18 
 
 10167 
 
 10000 
 
 10080 
 
 + 80 
 
 1070 
 
 942 
 
 -128 
 
 19 
 
 8348 
 
 8930 
 
 9138 
 
 +208 
 
 879 
 
 1043 
 
 +164 
 
 20 
 
 7076 
 
 8051 
 
 8095 
 
 + 44 
 
 745 
 
 958 
 
 +213 
 
 21 
 
 8709 
 
 7306 
 
 7137 
 
 -169 
 
 916 
 
 858 
 
 - 58 
 
 22 
 
 7441 
 
 6390 
 
 6279 
 
 -111 
 
 783 
 
 766 
 
 - 17 
 
 23 
 
 6872 
 
 5607 
 
 5513 
 
 - 94 
 
 723 
 
 677 
 
 - 46 
 
 24 
 
 6019 
 
 4884 
 
 4836 
 
 - 48 
 
 634 
 
 600 
 
 - 34 
 
 25 
 
 5315 
 
 4250 
 
 4236 
 
 - 14 
 
 559 
 
 529 
 
 - 30 
 
 26 
 
 4441 
 
 3691 
 
 3707 
 
 + 16 
 
 468 
 
 465 
 
 - 3 
 
 27 
 
 3810 
 
 3223 
 
 3242 
 
 + 19 
 
 401 
 
 410 
 
 + 9 
 
 28 
 
 3677 
 
 2822 
 
 2832 
 
 + 10 
 
 387 
 
 358 
 
 - 29 
 
 29 
 
 2622 
 
 2435 
 
 2474 
 
 + 39 
 
 276 
 
 315 
 
 + 39 
 
 30 
 
 2869 
 
 2159 
 
 2159 
 
 
 
 302 
 
 276 
 
 - 26 
 
 31 
 
 1847 
 
 1857 
 
 1883 
 
 + 26 
 
 194 
 
 242 
 
 + 48 
 
 32 
 
 2076 
 
 1663 
 
 1641 
 
 - 22 
 
 219 
 
 211 
 
 - 8 
 
 33 
 
 1666 
 
 1444 
 
 1430 
 
 - 14 
 
 175 
 
 185 
 
 + 10 
 
 34 
 
 1508 
 
 1269 
 
 1245 
 
 - 24 
 
 159 
 
 162 
 
 + 3 
 
 35 
 
 1568 
 
 1110 
 
 1083 
 
 - 27 
 
 165 
 
 142 
 
 - 23 
 
 36 
 
 1243 
 
 945 
 
 941 
 
 - 4 
 
 131 
 
 124 
 
 - 7 
 
 37 
 
 944 
 
 814 
 
 817 
 
 + 3 
 
 99 
 
 110 
 
 + 11 
 
 38 
 
 1056 
 
 715 
 
 707 
 
 - 8 
 
 111 
 
 96 
 
 - 15 
 
 39 
 
 725 
 
 604 
 
 611 
 
 + 7 
 
 77 
 
 87 
 
 + 10 
 
 40 
 
 1040 
 
 527 
 
 524 
 
 - 3 
 
 109 
 
 77 
 
 - 32 
 
 41 
 
 607 
 
 418 
 
 447 
 
 + 29 
 
 64 
 
 69 
 
 + 5 
 
 42 
 
 816 
 
 354 
 
 378 
 
 + 24 
 
 86 
 
 64 
 
 - 18 
 
 43 
 
 734 
 
 268 
 
 314 
 
 + 46 
 
 77 
 
 59 
 
 - 18 
 
 44 
 
 1075 
 
 191 
 
 255 
 
 + 69 
 
 113 
 
 54 
 
 - 59 
 
 45 
 
 737 
 
 78 
 
 201 
 
 +123 
 
 78 
 
 50 
 
 - 28 
 
 46 
 
 88 
 
 
 
 
 
 
 
 47 
 
 86 
 
 
 
 
 
 
 
 48 
 
 78 
 
 
 
 
 
 
 
 49 
 
 45 
 
 
 
 
 
 
 
 50 & 
 
 237 
 
 
 
 
 
 
 
 over. 
 
 
 
 
 
 
 
 
22 
 
 AGES OF VOLUNTEERS. 
 
 TABLE XIV. 
 
 Ages of Wisconsin and Iowa Volunteers. 
 
 Age 
 
 at last 
 
 birthday. 
 
 Number 
 
 at each year 
 
 of age. 
 
 Proportion at and over 
 specified age. 
 
 Observed. Calculated. 
 
 Difference. 
 (C.-0.) 
 
 Proportion at each year 
 of age. 
 
 Observed. Calculated. 
 
 Difference. 
 (C.-O.) 
 
 13 
 
 11 
 
 
 
 
 
 
 
 14 
 
 22 
 
 
 
 
 
 
 
 15 
 
 79 
 
 
 
 
 
 
 
 16 
 
 369 
 
 
 
 
 
 
 
 17 
 
 829 
 
 
 
 
 
 
 
 18 
 
 11083 
 
 10000 
 
 10000 
 
 
 
 1485 
 
 1221 
 
 -264 
 
 19 
 
 6440 
 
 8515 
 
 8779 
 
 +264 
 
 863 
 
 1048 
 
 +185 
 
 20 
 
 4874 
 
 7652 
 
 7731 
 
 + 79 
 
 653 
 
 902 
 
 +249 
 
 21 
 
 7082 
 
 6999 
 
 6829 
 
 -170 
 
 949 
 
 778 
 
 -171 
 
 22 
 
 5271 
 
 6050 
 
 6050 
 
 
 
 707 
 
 673 
 
 - 34 
 
 23 
 
 4240 
 
 5343 
 
 5377 
 
 + 34 
 
 569 
 
 585 
 
 + 16 
 
 24 
 
 3718 
 
 4774 
 
 4792 
 
 + 18 
 
 499 
 
 510 
 
 + 11 
 
 25 
 
 3260 
 
 4275 
 
 4282 
 
 + 7 
 
 437 
 
 447 
 
 + 10 
 
 26 
 
 2953 
 
 3838 
 
 3835 
 
 - 3 
 
 396 
 
 893 
 
 - 3 
 
 27 
 
 2675 
 
 3442 
 
 3442 
 
 
 
 359 
 
 345 
 
 - 14 
 
 28 
 
 2495 
 
 3083 
 
 3097 
 
 + 14 
 
 334 
 
 310 
 
 - 24 
 
 29 
 
 1844 
 
 2749 
 
 2787 
 
 + 38 
 
 247 
 
 277 
 
 + 30 
 
 30 
 
 1973 
 
 2502 
 
 2510 
 
 + 8 
 
 264 
 
 250 
 
 - 14 
 
 31 
 
 1472 
 
 2238 
 
 2260 
 
 + 22 
 
 196 
 
 227 
 
 + 31 
 
 32 
 
 1674 
 
 2042 
 
 2033 
 
 - 9 
 
 224 
 
 207 
 
 - 17 
 
 33 
 
 1432 
 
 1818 
 
 1826 
 
 + 8 
 
 192 
 
 191 
 
 - 1 
 
 34 
 
 1237 
 
 1626 
 
 1635 
 
 + 9 
 
 166 
 
 177 
 
 + 11 
 
 35 
 
 1359 
 
 1460 
 
 1458 
 
 - 2 
 
 182 
 
 165 
 
 - 17 
 
 36 
 
 1154 
 
 1278 
 
 1293 
 
 + 15 
 
 155 
 
 155 
 
 
 
 37 
 
 1022 
 
 1123 
 
 1138 
 
 + 15 
 
 137 
 
 146 
 
 + 9 
 
 38 
 
 1104 
 
 986 
 
 992 
 
 + 6 
 
 148 
 
 139 
 
 - 9 
 
 39 
 
 873 
 
 838 
 
 853 
 
 + 15 
 
 117 
 
 133 
 
 + 16 
 
 40 
 
 967 
 
 721 
 
 720 
 
 - 1 
 
 130 
 
 128 
 
 - 2 
 
 41 
 
 670 
 
 591 
 
 592 
 
 + 1 
 
 90 
 
 124 
 
 + 34 
 
 42 
 
 886 
 
 501 
 
 468 
 
 - 33 
 
 119 
 
 120 
 
 + 1 
 
 43 
 
 950 
 
 382 
 
 348 
 
 - 34 
 
 127 
 
 117 
 
 - 10 
 
 44 
 
 1374 
 
 255 
 
 231 
 
 - 24 
 
 184 
 
 114 
 
 - 70 
 
 45 
 
 531 
 
 71 
 
 117 
 
 + 46 
 
 71 
 
 112 
 
 + 41 
 
 46 
 
 113 
 
 
 
 
 
 
 
 47 
 
 108 
 
 
 
 
 
 
 
 48 
 
 115 
 
 
 
 
 
 
 
 49 
 
 76 
 
 
 
 
 
 
 
 50 & 
 
 632 
 
 
 
 
 
 
 
 over. 
 
 
 
 
 
 1 
 
 
 
AGES OF VOLUNTEERS. 23 
 
 The agreement of these several special results with those de- 
 duced from their aggregate is remarkable. Only in one case, 
 that of the Illinois troops, has the simple formula 
 
 s n = a — bn -\- ch n 
 
 failed to give all desired accordance between theory and observa- 
 tion ; and throughout the whole series the same peculiarities in 
 the residuals are recognizable. In this connection I may add, 
 what is in itself very significant, that attempts to deduce a law 
 of distribution of age for troops recruited in Missouri, Kentucky, 
 Tennessee, and Virginia have proved fruitless, and only small 
 success was attainable for the Maryland volunteers. The infer- 
 ence is obvious, that the volunteering of troops from these States 
 was not subject to the undisturbed influence of any statistical 
 law. In the case of Illinois troops, a curious anomaly manifested 
 itself in the residuals, namely, a cyclical or periodic term. This 
 was found to be represented with sufficient accuracy by adding 
 to the formula a term d sin *i/n ■ 68°, in which d = 314. I know 
 of no satisfactory interpretation of this expression, but it has been 
 used in the preparation of the table for that State. 
 
 In Table XV. is presented a summary of the results deduced 
 from the special groups presented in Tables III. to XIV. All 
 the constants are reduced to the same scale, and hold good for 
 10 000 troops of the ages 18 to 45 at last birthday, inclusive. 
 The mean ages, as here given, refer, not to the last birthday, but 
 to the actual date of enlistment. 
 
 The values of the constants for these special tables have been 
 determined from a smaller number of equations of condition 
 than were used for the grand total. In that each year was spe- 
 cially used ; in these the results were deduced from eight normal 
 places. 
 
24 
 
 AGES OF VOLUNTEERS. 
 
 TABLE XV. 
 
 Constants deduced for Special Glasses of Volunteers. 
 
 
 Number of Sol- 
 diers 
 
 Mean age at en- 
 listment. 
 
 
 
 
 
 Class. 
 
 
 
 
 a. 
 
 6. 
 
 C. 
 
 h. 
 
 
 Of all 
 ages. 
 
 Of mili- 
 tary age. 
 
 For all. 
 25.8362 
 
 For 
 18 to 45. 
 
 25.8083 
 
 
 
 
 
 | Total Enlisted Men 
 
 1012273 
 
 996647 
 
 2102.8 
 
 77.04 
 
 7897.2 
 
 0.8536 
 
 Total Infantry 
 
 785120 
 
 773271 
 
 25.7827 
 
 25.7484 
 
 2080.0 
 
 75.84 
 
 7920.0 
 
 0.8514 
 
 Total Cavalry 
 
 117405 
 
 115951 
 
 25.8110 
 
 25.7795 
 
 1595.0 
 
 57.90 
 
 8405.0 
 
 0.8593 
 
 Total Artillery 
 
 42862 
 
 42357 
 
 26.1576 
 
 26.1202 
 
 2239.0 
 
 81.20 
 
 7761.0 
 
 0.8585 
 
 Me., N.H., Vt., Conn. 
 
 76445 
 
 75881 
 
 25.8792 
 
 25.8423 
 
 2112.0 
 
 73.06 
 
 7S89.0 
 
 0.8511 
 
 Massachusetts 
 
 54705 
 
 54137 
 
 26.0561 
 
 26.0943 
 
 2016.0 
 
 76-40 
 
 7984.0 
 
 0.8662 
 
 New York 
 
 183281 
 
 181594 
 
 26.130S 
 
 26.1642 
 
 2390.5 
 
 88.86 
 
 7609.5 
 
 0.8575 
 
 Pennsylvania 
 
 116043 
 
 114844 
 
 25.8227 
 
 25.8331 
 
 2477.4 
 
 90.20 
 
 7523.0 
 
 0.8340 
 
 Ohio 
 
 153133 
 
 149936 
 
 25.4936 
 
 25.3859 
 
 2625.0 
 
 96.08 
 
 7375.0 
 
 0.8287 
 
 Indiana 
 
 70673 
 
 69536 
 
 24.7100 
 
 24.6858 
 
 1175.0 
 
 42.18 
 
 8825.0 
 
 0.8409 
 
 1 Michigan 
 
 39107 
 
 38489 
 
 25.5290 
 
 25.5276 
 
 1827.0 
 
 61.30 
 
 8173.0 
 
 0.8510 
 
 Illinois 
 
 96409 
 
 95003 
 
 25.9369 
 
 25.8935 
 
 2023.0 
 
 70.66 
 
 8057.0 
 
 0.S558 
 
 j Wisconsin and Iowa 
 
 76987 
 
 74613 
 
 26.1571 
 
 25.9991 
 
 2737.0 
 
 100.20 
 
 7263.0 
 
 0.8456 
 
 In considering the residuals, the most striking feature is the 
 excess of the recorded numbers at 18 and 21, which latter excess 
 is counterbalanced by a deficiency at 20 and to some extent at 19 
 also. The explanation of this is readily found in the facts that 
 enlistments of youths under 18 are not valid without the formal 
 consent of parents, and that 21 is the period at which minority 
 ceases. There can be no reasonable doubt that these residuals 
 furnish the measure of the number under 18 and under 21, who 
 misstated their age to the mustering officer. At the age of 18 
 the discordance is less marked than at 21, since the inducements 
 to misstate operated near this age in different directions, many of 
 those at 18 probably representing themselves as 21 years old, 
 while' their number was made good by others who untruly 
 declared themselves as having completed their 18th year. 
 
 The excess of the recorded number at 21 averages 1| per cent., 
 that deficiency at 20 is about 2 per cent., and at 19 about If per 
 cent. The number recorded for 18 years is in excess by 1 per 
 cent., although it varies very considerably in the different groups. 
 
 A large excess, representing the number of those who from 
 similar motives understated their ages, is also to be seen at the age 
 
AGES OF VOLUNTEERS. 25 
 
 of 44 in most States, corresponding to an analogous deficiency at 
 45. This varies, however, in different States, owing in all proba- 
 bility to the different interpretation by the mustering officers of 
 that provision of the law which precluded the acceptance of men 
 over 45 years old. The average, in the more elaborately calcu- 
 lated table for the grand total, places the number at 44 in excess 
 of the computed number by two thirds of its whole amount, and 
 leaves that at 45 in defect by one fourth part. 
 
 For all other ages than those enumerated, the regular excess or. 
 defect of the residuals furnishes apparently the measure of the 
 accuracy with which the ages were stated or recorded. It will be 
 seen that at those ages which correspond to what are called round 
 numbers, such as those divisible by 10, also, though to a less 
 extent, at those divisible by 5, and in a still less but yet recog- 
 nizable degree, at those divisible by 2, the recorded numbers are 
 in excess; while the adjacent numbers, especially those ending in 
 1, 9, and 7, are in defect. The natural tendency which every one 
 will recognize, and which inclines us to make use of certain more 
 habitually employed numbers, rather than to use a minuteness 
 repugnant to some persons, furnishes an adequate and, as I believe, 
 the true explanation. 
 
 It will be readily noted that where any two of the above-named 
 principles conflict, the residual is diminished ; and that where they 
 act in combination it is increased. 
 
 Lines showing the computed and the enrolled numbers of 
 enlisted men are given on Chart A, and readily manifest these 
 facts to the eye. The other data upon this chart are given for 
 comparison, and will be referred to hereafter. It will be borne 
 in mind that the numbers given do not, by a large amount, repre- 
 sent the actual numbers of enlisted volunteers or of volunteer 
 officers, nor probably so much as two fifths of the total number 
 of our soldiers in the struggle for national existence. They are 
 relative quantities, deduced from only those data cited at the com- 
 mencement of this paper, and illustrate, not the actual numbers 
 for our troops, but the relative distribution of their ages. 
 
 The same results are presented in another form upon Chart B, 
 which exhibits, for the enlisted men, the officers, and the white 
 male population, the proportion at and over the specified ages and 
 under 45 years, for each 10 000 men of military age. 
 
26 AGES OF VOLUNTEERS. 
 
 Charts C and B show the law by which the ratios of officers 
 and enlisted men to the white male population vary with the age. 
 All the numbers are reduced to the scale of ten thousand of pop- 
 ulation at 18 years, Chart being constructed in reference to 
 the whole United States, and Chart D to the Loyal States only. 
 
 3. Ages of Officers. 
 
 The total number of officers of all ages is 37 184, that of those 
 between 18 and 46 being 35953. 
 
 On comparing the numbers at the several ages with the formula 
 
 s n = a — bn-\- ch n 
 
 we find at once that for certain ages the value of h would be an 
 impossible one ; and that for other years, which would yield possible 
 values, these values are so discordant and the residuals to which 
 they lead become so large that it is manifest that the curve can be 
 represented neither by this nor by any similar law. 
 Many trials have led to the empirical formula 
 
 s n = a — bn* -4- c sin n k 8 (A) 
 
 as that which best represents the character of the curve. The 
 extremely complicated manner, however, in which the six constants 
 of this equation enter into the formula renders the attainment of 
 a solution from six equations, by any direct process, a matter of 
 great difficulty and inconvenience. Of course the constant a rep- 
 resents the value of *„ for n = 0, so that the problem really con- 
 sists in the determination of the five quantities b, c, &', k, and 0. 
 Graphic representations of the curve, by showing the points at 
 which the third term becomes =0, facilitated the approximate 
 determination of these constants, and thus equations of condition 
 were formed which have led to quite satisfactory values, giving 
 an agreement between the formula and the observed numbers 
 nearly if not quite as good as that obtained for the enlisted men 
 by the formula already described. 
 
 Subsequently, investigations made for the purpose of extending 
 this formula to the ages from 46 to 50 showed a deviation for these 
 later years. This* deviation seems only to be reconciled by the 
 employment of an additional term containing two more constants, 
 
AGES OF VOLUNTEERS. 27 
 
 and the term thus found proves applicable to all ages above 30, 
 essentially diminishing the residuals for all subsequent years. 
 The formula then stands for each 10 000 officers 
 
 s„=10 000 — 736rc a75 + 1259 sinrc 0536 x 45°.64+ 100 sin (n— 12)18° 
 
 in which the last term is only to be employed for positive values 
 of n — 12, that is, for ages above 30 years. 
 
 The near agreement of this formula with the observations will 
 be recognized on Table XVI., which exhibits for each year of age 
 from 18 to 50, as well as for those above 50, the actual and the 
 proportionate observed number of officers, both at, and at and over, 
 the given age, together with the corresponding numbers as deduced 
 from the formula, and the discordances between Computation and 
 Observation. 
 
 The dissimilarity of the curves thus found for officers and for 
 enlisted men is most striking, as will be perceived by reference to 
 Charts A and B. The chief discordance for the officers' curve is 
 for the age of 18 years, at which, or at 19, the formula seems to 
 fail. This is probably due in part to the fact that comparatively 
 few officers were commissioned under the age of legal maturity, 
 so that the law governing the distribution by age ought not to be 
 regarded as applicable below 21 years. 
 
28 AGES OF VOLUNTEERS. 
 
 TABLE XVI. 
 
 Ages of Officers of United States Volunteers. 
 
 Age 
 
 at last 
 
 birthday. 
 
 Number 
 
 at given 
 
 age. 
 
 Pro] 
 Observed. 
 
 aortion at 
 age 
 
 Calcu- 
 lated. 
 
 given 
 
 Difference. 
 (G.-O.) 
 
 Number 
 at and over 
 given age. 
 
 Propc 
 Observed. 
 
 rtion at an 
 given age 
 
 Calcu- 
 lated. 
 
 d over 
 
 Difference. 
 (C.-O.) 
 
 13 
 
 
 
 
 
 
 
 
 
 14 
 
 
 
 
 
 
 
 
 
 15 
 
 1 
 
 
 
 
 37183 
 
 
 
 
 16 
 
 5 
 
 
 
 
 37182 
 
 
 
 
 17 
 
 5 
 
 
 
 
 37177 
 
 
 
 
 18 
 
 178 
 
 48 
 
 -164 
 
 -212 
 
 37172 
 
 10000 
 
 10000 
 
 
 
 19 
 
 409 
 
 110 
 
 +233 
 
 4123 
 
 37094 
 
 9952 
 
 10164 
 
 +212 
 
 20 
 
 687 
 
 185 
 
 351 
 
 +166 
 
 36685 
 
 9842 
 
 9931 
 
 + 89 
 
 21 
 
 1630 
 
 439 
 
 443 
 
 + 4 
 
 35998 
 
 9657 
 
 9580 
 
 - 77 
 
 22 
 
 1839 
 
 495 
 
 500 
 
 + 5 
 
 34368 
 
 9218 
 
 9137 
 
 - 81 
 
 23 
 
 2101 
 
 565 
 
 537 
 
 - 28 
 
 32529 
 
 8723 
 
 8637 
 
 - 86 
 
 24 
 
 2234 
 
 601 
 
 557 
 
 - 44 
 
 30428 
 
 8158 
 
 8100 
 
 - 58 
 
 25 
 
 2161 
 
 581 
 
 567 
 
 - 14 
 
 28194 
 
 7557 
 
 7543 
 
 - 14 
 
 26 
 
 2114 
 
 569 
 
 563 
 
 - 6 
 
 26033 
 
 6976 
 
 6976 
 
 
 
 27 
 
 1968 
 
 529 
 
 555 
 
 + 26 
 
 23919 
 
 6407 
 
 6413 
 
 + 6 
 
 28 
 
 2071 
 
 557 
 
 536 
 
 - 21 
 
 21951 
 
 5878 
 
 5858 
 
 - 20 
 
 29 
 
 1756 
 
 472 
 
 516 
 
 + 44 
 
 19880 
 
 5321 
 
 5322 
 
 + 1 
 
 30 
 
 1836 
 
 494 
 
 457 
 
 - 37 
 
 18124 
 
 4849 
 
 4806 
 
 - 43 
 
 31 
 
 1429 
 
 884 
 
 430 
 
 + 46 
 
 16288 
 
 4355 
 
 4349 
 
 - 6 
 
 32 
 
 1613 
 
 434 
 
 405 
 
 - 29 
 
 14859 
 
 3971 
 
 3919 
 
 - 52 
 
 33 
 
 1422 
 
 383 
 
 381 
 
 - 2 
 
 13246 
 
 3537 
 
 3514 
 
 - 23 
 
 34 
 
 1324 
 
 356 
 
 359 
 
 + 3 
 
 11824 
 
 3154 
 
 3133 
 
 - 21 
 
 35 
 
 1434 
 
 386 
 
 335 
 
 - 51 
 
 10500 
 
 2798 
 
 2774 
 
 - 24 
 
 36 
 
 1221 
 
 328 
 
 313 
 
 - 15 
 
 9066 
 
 2412 
 
 2439 
 
 + 27 
 
 37 
 
 1031 
 
 277 
 
 291 
 
 + 14 
 
 7845 
 
 2084 
 
 2126 
 
 + 42 
 
 38 
 
 1033 
 
 278 
 
 269 
 
 - 9 
 
 6814 
 
 1807 
 
 1835 
 
 + 28 
 
 39 
 
 813 
 
 219 
 
 245 
 
 + 26 
 
 5781 
 
 1529 
 
 1566 
 
 + 37 
 
 40 
 
 874 
 
 235 
 
 222 
 
 - 13 
 
 4968 
 
 1310 
 
 1321 
 
 + 11 
 
 41 
 
 557 
 
 149 
 
 197 
 
 + 48 
 
 4094 
 
 1075 
 
 1099 
 
 + 24 
 
 42 
 
 656 
 
 176 
 
 171 
 
 - 5 
 
 3537 
 
 926 
 
 902 
 
 - 24 
 
 43 
 
 485 
 
 130 
 
 148 
 
 + 18 
 
 2881 
 
 750 
 
 731 
 
 - 19 
 
 44 
 
 598 
 
 161 
 
 124 
 
 - 37 
 
 2396 
 
 620 
 
 583 
 
 - 37 
 
 45 
 
 478 
 
 130 
 
 100 
 
 - 30 
 
 1798 
 
 459 
 
 459 
 
 
 
 46 
 
 217 
 
 58 
 
 86 
 
 + 28 
 
 1320 
 
 329 
 
 359 
 
 + 30 
 
 47 
 
 184 
 
 50 
 
 70 
 
 + 20 
 
 1103 
 
 271 
 
 273 
 
 + 2. 
 
 48 
 
 17.5 
 
 47 
 
 58 
 
 + 11 
 
 919 
 
 221 
 
 203 
 
 - 18 
 
 49 
 
 121 
 
 33 
 
 55 
 
 + 22 
 
 744 
 
 174 
 
 145 
 
 - 29 
 
 50 & 
 
 523 
 
 141 
 
 90 
 
 - 51 
 
 523 
 
 141 
 
 90 
 
 - 51 
 
 over. 
 
 
 
 
 
 
 
 
 
AGES OF VOLUNTKKliS. 
 
 29 
 
 The mean age at last birthday for all the officers is . 30.4406 
 " " " for those between 18 & 45 29.8338 
 
 and the mean age of the mean at last birthday is . 29.45 
 or about 29.94 at the time of their muster into the service. 
 Above and below this age the number of officers was equal. 
 
 The annexed Table XVII. exhibits the relative proportions of 
 officers to the enlisted men, and of these to the white male popu- 
 lation of the whole United States and of the Loyal States respec- 
 tively, as given by the census of 1860, taken less than one year 
 before the call to arms. 
 
 The caution must here be repeated, that the " proportion of 
 enlisted men to the population," as here given, does not at all 
 apply to the armies of the nation during the rebellion. It relates 
 solely to the number of volunteer troops here considered ; and 
 this Table XVII. is presented solely to make manifest the laws 
 according to which the ratios of enlisted men to the population, 
 and the ratios of officers to men, varied with the age. 
 
 TABLE XVII. 
 
 Relative Proportions 
 of Officers, Enlisted Men, and White Male Population, 
 for the first million of Volunteers. 
 
 AGE. 
 
 Proportion of 
 
 Officers to 
 
 Enlisted 
 
 Men. 
 
 Proportion 
 of Enlisted 
 Men to Popu- 
 lation of 
 U. States. 
 
 Proportion 
 of Enlisted 
 
 Men to Pop- 
 ulation of 
 
 Loyal States. 
 
 AGE. 
 
 Proportion of 
 
 Officers to 
 
 Enlisted 
 
 Men. 
 
 Proportion 
 of Enlisted 
 Men to Popu- 
 lation of 
 U. States. 
 
 Proportion ' 
 of Enlisted 
 
 Men to Pop- 
 ulation of 
 
 Loyal States. 
 
 18 
 
 0.001 
 
 0.448 
 
 0.570 
 
 32 
 
 0.072 
 
 0.100 
 
 0.128 
 
 19 
 
 0.007 
 
 0.393 
 
 0.502 
 
 33 
 
 0.074 
 
 0.093 
 
 0.119 
 
 20 
 
 0.013 
 
 0.345 
 
 0.442 
 
 34 
 
 0.076 
 
 0.088 
 
 0.112 
 
 21 
 
 0.019 
 
 0.305 
 
 0.391 
 
 35 
 
 0.077 
 
 0.084 
 
 0.105 
 
 22 
 
 0.025 
 
 0.269 
 
 0.363 
 
 36 
 
 0.078 
 
 0.080 
 
 0.100 
 
 23 
 
 0.031 
 
 0.239 
 
 0.308 
 
 37 
 
 0.077 
 
 0.077 
 
 0.096 
 
 24 
 
 0.037 
 
 0.212 
 
 0.275 
 
 38 
 
 0.075 
 
 0.075 
 
 0.093 
 
 25 
 
 0.043 
 
 0.190 
 
 0.246 
 
 39 
 
 0.073 
 
 0.074 
 
 0.090 
 
 26 
 
 0.04S 
 
 0.170 
 
 0.221 
 
 40 
 
 0.068 
 
 0.073 
 
 0.088 
 
 27 
 
 0.054 
 
 0.154 
 
 0.199 
 
 41 
 
 0.062 
 
 0.073 
 
 0.088 
 
 28 
 
 0.969 
 
 0.139 
 
 0.180 
 
 42 
 
 0.057 
 
 0-07-3 
 
 0.087 
 
 29 
 
 0.063 
 
 0.127 
 
 0.164 
 
 43 
 
 0.049 
 
 0.074 
 
 0.087 
 
 30 
 
 0.065 
 
 0.116 
 
 0.150 
 
 44 
 
 0.041 
 
 0.075 
 
 0.088 
 
 31 
 
 0.068 
 
 0.107 
 
 0.138 
 
 45 
 
 0.033 
 
 0.076 
 
 0.089 
 
30 AGES OF VOLUNTEERS. 
 
 4. Population of the United States and of the Loyal States. 
 
 The great and unexpected dissimilarity between the law of dis- 
 tribution of age for officers and for men led, as I have already 
 mentioned, to an investigation of the ages of the white male pop- 
 ulation, both of the whole United States, and of the Loyal States 
 considered by themselves. And, in the absence of any distinct 
 criterion, those States which were free from slavery in 1860, to- 
 gether with Delaware, Maryland, Kentucky, and Missouri, have 
 been classed as Loyal States. The territory of West Virginia, 
 eastern Tennessee, &c, is thus excluded, although inhabited by 
 a thoroughly loyal population, which contributed about twenty of 
 the regiments here computed ; and about ten other regiments, 
 included in our data, were raised in States not accounted loyal. 
 But all these are offset by the very considerable portion of the 
 inhabitants of the four Slave States above named, from which the 
 insurgent army was reinforced. 
 
 The only materials available for the inquiry are contained in 
 the tables, derived from the official census of the United States 
 in 1860. Of course it is the male population alone which has any 
 relation to the present research. 
 
 The difficulty of deducing from these meagre details the num- 
 ber of males at each year of military age is apparent at the first 
 glance. Had the classification between the ages of 20 and 50 
 been in six groups of five years each, instead of three groups of 
 ten years, the facility and accuracy of the investigation would have 
 been incomparably greater. As it is, the only available data are 
 contained in the second column of the following tables, XVIII. 
 and XIX. These tables give, in column 9, the results of the 
 formulas obtained for representing the observed numbers given 
 in column 2. The degree of correctness of these formulas may 
 be estimated by means of column 4, which shows the excess of 
 the calculated number over the number given by the census, in 
 decimals of the latter. The accordance for ages above 20 years is 
 remarkably good. Beyond 50 years the agreement is not so close 
 as between 20 and 50, but is nevertheless quite tolerabll ; but the 
 comparison is omitted here as not pertinent to the subject, since 
 none of the census-numbers for groups of ages above 50 have 
 been employed in the computation. 
 
AGES OF VOLUNTEERS. 
 
 31 
 
 The other columns require no explanation. It will be remem- 
 bered that the numbers of enlisted men and officers here given 
 are merely those belonging to the original volunteer regiments at 
 the time of their enlistment, excluding all recruits, substitutes, 
 drafted men, &c. Also, that the numbers apply only to those 
 regiments which had been mustered into the United States ser- 
 vice prior to the collection of our data, as shown on page 2. 
 
 TABLE XVIII. 
 
 White Male Population of the United States in 1860. 
 
 Comparison between Computed and Observed Ages. 
 
 Age at last 
 birthday. 
 
 White Male 
 of the Uni 
 
 Census. 
 
 Population 
 ted Stales. 
 
 Computed. 
 
 Difference. 
 (C.-O.) 
 
 Enlisted 
 Men of first 
 volunteers. 
 
 Officers of 
 first vol- 
 unteers. 
 
 Ratio to White Male 
 Population. 
 
 Men. Officers. 
 
 10- 15 
 
 1 578 274 
 
 1 547 730 
 
 -0.0193 
 
 
 
 
 
 15-20 
 
 1 391 950 
 
 1 422 340 
 
 +0.0245 
 
 
 
 
 
 18-20 
 
 
 553 360 
 
 
 219 200 
 
 587 
 
 0.395 
 
 0.0011 
 
 20-30 
 
 2 465 276 
 
 2 436 770 
 
 -0.0116 
 
 529 809 
 
 18 561 
 
 0.217 
 
 0.0076 
 
 30-40 
 
 1 847 259 
 
 1 847 810 
 
 0.0000 
 
 165 292 
 
 13 156 
 
 0.090 
 
 0.0071 
 
 40-45 
 
 
 807 860 
 
 
 63 607 
 
 
 0.079 
 
 
 40-50 
 
 1 215 031 
 
 1 216 690 
 
 +0.0014 
 
 
 4 868 
 
 
 0.0040 
 
 18 - 45 
 
 
 5 645 800 
 
 
 977 968 
 
 
 
 
 TABLE XIX. 
 
 White Male Population of the Loyal States in 1860. 
 
 Comparison between Computed and Observed Ages. 
 
 Age at last 
 birthday. 
 
 White Male 
 of the L03 
 
 Census. 
 
 Population 
 al States. 
 
 Computed. 
 
 Difference. 
 (C.-O.) 
 
 Enlisted 
 Men of first 
 volunteers. 
 
 Officers of 
 first vol- 
 unteers. 
 
 Ratio to 
 Popr. 
 
 Men. 
 
 SVhite Male 
 
 lation. 
 
 Officers. 
 
 10-15 
 
 1 211 521 
 
 1 179 260 
 
 -0.0266 
 
 
 
 
 
 15-20 
 
 1 095 934 
 
 1 110 770 
 
 +0.0135 
 
 
 
 
 
 18-20 
 
 
 435 100 
 
 
 219 200 
 
 587 
 
 0.502 
 
 0.0014 
 
 20-30 
 
 1 971 486 
 
 1 956 890 
 
 -0.0075 
 
 529 809 
 
 18 561 
 
 0.271 
 
 0.0095 
 
 30-40 
 
 1 517 736 
 
 1 517 720 
 
 0.0000 
 
 165 292 
 
 13 156 
 
 0.109 
 
 0.0087 
 
 40-45 
 
 • 
 
 664 510 
 
 
 63 667 
 
 
 0.096 
 
 
 40 - 50 
 
 996 481 
 
 996 350 
 
 0.0000 
 
 
 4 868 
 
 
 0.0049 
 
 18 - 45 
 
 
 4 574 220 
 
 
 977 968 
 
 
 
 
32 AGES OF VOLUNTEERS. 
 
 The formulas which thus represent the number of white males 
 from the age of 10 years upwards are, — 
 
 for the United States 
 
 x = 445440 sin (134° 34' -f- (y — 10) • 52') 
 
 for the Loyal States 
 
 x = 257 870 sin (111° 6"'.l -p (y — 10) • 80'.2) 
 
 in which x is the number at the year of age y. 
 
 Assuming these values to be correct, we find the distribution 
 of the white male population in 1860 to have been as represented 
 in Tables XX. and XXI. 
 
 These tables show, for the United States and the Loyal States 
 respectively, the actual numbers : — first, at each year of age 
 from 15 to 50, inclusive ; secondly, at and over each year of age 
 from 15 to 50, inclusive ; thirdly, at and over each year within 
 the limits of military age from 18 upwards, and also the cor- 
 responding relative or proportional numbers, using those for 18 
 years as the units. 
 
 Subsequent investigation has led to the detection of a formula 
 totally different in structure from those above given, but which, 
 although its agreement with the census-numbers within the years 
 of military age is by no means so close as these afford, yet repre- 
 sents the various censuses of the United States and those of for- 
 eign countries throughout the period of human life with a degree 
 of precision never before attained, so far as I am aware. It rep- 
 resents the number of infants under one year as well as, and 
 indeed better than, the number at middle life or advanced years ; 
 and I cannot avoid the conviction that this formula affords an im- 
 portant step toward the true mathematical expression of what we 
 may call the life-curve. Modifications will doubtless be made in 
 it ; indeed, it manifestly gives the numbers too small for the ages 
 under 5 years, over 70 years, and between 20 and 45 years, while 
 those of later childhood and youth on the one side, and of ad- 
 vanced maturity on the other, are in excess. But the discor- 
 dances are small, and I hardly think that any expression of equal 
 simplicity will be found which will represent the life-curve more 
 closely. 
 
AGES OF VOLUNTEERS. 33 
 
 Of this formula, which is simply 
 
 s n = a sin n k" 8 
 
 where s n represents the sum of all under the age n, a is the total 
 number, and k, 6 are two constants characteristic of the especial 
 population under examination, details and applications are given 
 in the Appendix ; where also are tables exhibiting the distribution 
 of the total white male population of the United States and of the 
 Loyal States, as given by this law. The values differ slightly from 
 those in Tables XXI. and XXII., which, for the census of 1860 
 at least, seem to be more accurate within the limits to which 
 they are extended, although the corresponding numbers beyond 
 these limits would be less accordant with observation. 
 
34 
 
 AGES OF VOLUNTEERS. 
 
 TABLE XX. 
 
 White Male Population of the United States in 1860. 
 
 Age 
 
 at last 
 
 birthday 
 
 Actual Number 
 
 15 
 
 16 
 17 
 18 
 
 19 
 
 20 
 
 21 
 
 22 
 
 23 
 
 24 
 
 25 
 
 26 
 
 27 
 
 2S 
 
 29 
 
 30 
 
 31 
 
 32 
 
 33 
 
 34 
 
 35 
 
 36 
 
 37 
 
 38 
 
 39 
 
 40 
 
 41 
 
 42 
 
 43 
 
 44 
 
 45 
 
 46 
 
 47 
 
 48 
 
 49 
 
 50 
 
 At the 
 given age. 
 
 294 770 
 
 289 680 
 
 284 530 
 
 279 320 
 
 274 040 
 
 268 700 
 
 263 290 
 
 257 820 
 
 252 300 
 
 246 720 
 
 241 090 
 
 235 380 
 
 229 640 
 
 223 840 
 
 217 990 
 
 212 090 
 
 206 140 
 
 200 140 
 
 194 100 
 
 188 020 
 
 181 890 
 
 175 710 
 
 169 500 
 
 163 250 
 
 156 970 
 
 150 640 
 
 144 290 
 
 137 900 
 
 131 470 
 
 125 020 
 
 118 540 
 
 112 030 
 
 105 500 
 
 98 940 
 
 92 360 
 
 85 760 
 
 At aud o*ver 
 given age. 
 
 8 252 612 
 7 957 842 
 7 668 162 
 7 383 632 
 7 104 312 
 6 830 272 
 6 561 572 
 6 298 282 
 6 040 462 
 5 788 162 
 5 541 442 
 5 300 352 
 5 064 972 
 4 835 332 
 4 611 492 
 4 393 502 
 4 181 412 
 3 975 272 
 3 775 132 
 3 581 032 
 3 393 012 
 3 211 122 
 3 035 412 
 2 865 912 
 2 702 662 
 2 545 692 
 2 395 052 
 250 762 
 Iff 862 
 981 392 
 856 372 
 737 832 
 625 802 
 520 302 
 421 362 
 329 002 
 
 At and over 
 
 given age and 
 
 under 46. 
 
 5 645 800 
 
 5 366 480 
 
 5 092 440 
 
 4 823 740 
 
 4 560 450 
 
 4 302 630 
 
 4 050 330 
 
 3 803 610 
 
 3 562 520 
 
 3 327 140 
 
 3 097 500 
 
 873 660 
 
 655 670 
 
 443 5S0 
 
 237 440 
 
 037 300 
 
 1 843 200 
 
 1 655 180 
 
 1 473 290 
 
 1 297 580 
 
 1 128 080 
 
 964 830 
 
 807 860 
 
 657 220 
 
 512 930 
 
 375 030 
 
 243 560 
 
 118 540 
 
 Relative Number 
 
 At the 
 given age. 
 
 10 000 
 9 811 
 9 620 
 9 426 
 9 230 
 9 033 
 8 833 
 8 631 
 8 427 
 8 222 
 8 014 
 
 804 
 593 
 380 
 165 
 949 
 6 731 
 6 512 
 291 
 068 
 845 
 620 
 393 
 166 
 937 
 707 
 476 
 244 
 Oil 
 777 
 542 
 307 
 072 
 
 At and over 
 given age. 
 
 10 000 
 9 622 
 9 251 
 
 8 887 
 8 530 
 8 181 
 
 839 
 505 
 179 
 860 
 549 
 246 
 951 
 664 
 385 
 114 
 851 
 596 
 350 
 112 
 882 
 661 
 448 
 244 
 049 
 862 
 684 
 515 
 354 
 202 
 059 
 925 
 800 
 
 At and over 
 
 given age & 
 
 under 46. 
 
 10 000 
 9 505 
 9 020 
 8 544 
 
 8 078 
 
 621 
 174 
 737 
 310 
 893 
 486 
 090 
 704 
 328 
 963 
 609 
 265 
 932 
 610 
 299 
 999 
 1 710 
 1 432 
 1 165 
 909 
 665 
 432 
 210 
 
AGES OF VOLUNTEERS. 
 
 35 
 
 TABLE XXI. 
 
 White Male Population of the Loyal States in 1860. 
 
 Age 
 at last 
 birth- 
 day. 
 
 1 
 
 At the 
 given age. 
 
 Lctual Numb 
 
 At and over 
 given age. 
 
 er 
 
 At and over 
 
 given age 
 
 and under 46. 
 
 Re] 
 
 At the 
 given age. 
 
 ative Num 
 
 At and over 
 given age. 
 
 ber 
 
 At and over 
 jiven age & 
 under 46- 
 
 Prop to 
 W. Male 
 Pop. of 
 
 United 
 States. 
 
 15 
 
 228 120 
 
 6 675 533 
 
 
 
 
 
 
 7 739 
 
 16 
 
 225 270 
 
 6 447 413 
 
 
 
 
 
 
 7 776 
 
 17 
 
 222 280 
 
 6 222 143 
 
 
 
 
 
 
 7 812 
 
 18 
 
 219 160 
 
 5 999 863 
 
 4 574 220 
 
 10 000 
 
 10 000 
 
 10 
 
 000 
 
 7 846 
 
 19 
 
 215 940 
 
 5 780 703 
 
 4 355 060 
 
 9 853 
 
 9 634 
 
 9 
 
 521 
 
 7 880 
 
 20 
 
 212 600 
 
 5 564 763 
 
 4 139 120 
 
 9 700 
 
 9 275 
 
 9 
 
 049 
 
 7 912 
 
 21 
 
 209 130 
 
 5 352 163 
 
 3 926 520 
 
 9 542 
 
 8 920 
 
 8 
 
 584 
 
 7 943 
 
 22 
 
 205 550 
 
 5 143 033 
 
 3 717 390 
 
 9 379 
 
 8 572 
 
 8 
 
 127 
 
 7 973 
 
 23 
 
 201 870 
 
 4 937 483 
 
 3 511 840 
 
 9 211 
 
 8 229 
 
 7 
 
 678 
 
 8 001 
 
 24 
 
 198 070 
 
 4 735 613 
 
 3 309 970 
 
 9 038 
 
 7 893 
 
 7 
 
 237 
 
 8 028 
 
 25 
 
 194 160 
 
 4 537 543 
 
 3 111 900 
 
 8 859 
 
 7 563 
 
 6 
 
 804 
 
 8 054 
 
 26 
 
 190 150 
 
 4 343 383 
 
 2 917 740 
 
 8 676 
 
 7 239 
 
 6 
 
 379 
 
 8 078 
 
 27 
 
 186 040 
 
 4 153 233 
 
 2 727 590 
 
 ' 8 488 
 
 6 922 
 
 5 
 
 963 
 
 8 101 
 
 28 
 
 181 820 
 
 3 967 193 
 
 2 541 550 
 
 8 296 
 
 6 612 
 
 5 
 
 555 
 
 8 123 
 
 29 
 
 177 500 
 
 3 785 373 
 
 2 359 730 
 
 8 099 
 
 6 309 
 
 5 
 
 157 
 
 8 141 
 
 30 
 
 173 100 
 
 3 607 873 
 
 2 182 230 
 
 7 898 
 
 6 013 
 
 4 
 
 769 
 
 8 162 
 
 31 
 
 168 590 
 
 3 434 773 
 
 2 009 130 
 
 7 692 
 
 5 725 
 
 4 
 
 391 
 
 8 179 
 
 32 
 
 163 990 
 
 3 266 183 
 
 1 840 540 
 
 7 483 
 
 5 444 
 
 4 
 
 022 
 
 8 194 
 
 33 
 
 159 300 
 
 3 102 193 
 
 1 676 550 
 
 7 269 
 
 5 170 
 
 3 
 
 663 
 
 8 207 
 
 34 
 
 154 530 
 
 2 942 893 
 
 1 517 250 
 
 7 051 
 
 4 905 
 
 3 
 
 315 
 
 8 219 
 
 35 
 
 149 680 
 
 2 788 363 
 
 1 362 720 
 
 6 829 
 
 4 647 
 
 2 
 
 977 
 
 8 229 
 
 36 
 
 144 730 
 
 2 638 683 
 
 1 213 040 
 
 6 604 
 
 4 398 
 
 2 
 
 650 
 
 8 237 
 
 37 
 
 139 720 
 
 2 493 953 
 
 1 068 310 
 
 6 375 
 
 4 157 
 
 2 
 
 334 
 
 8 243 
 
 38 
 
 134 620 
 
 2 354 233 
 
 928 590 
 
 6 143 
 
 3 924 
 
 2 
 
 029 
 
 8 246 
 
 39 
 
 129 460 
 
 2 219 613 
 
 793 970 
 
 5 907 
 
 3 699 
 
 1 
 
 735 
 
 8 247 
 
 40 
 
 124 230 
 
 2 090 153 
 
 664 510 
 
 5 668 
 
 3 484 
 
 1 
 
 452 
 
 8 247 
 
 41 
 
 118 920 
 
 1 965 923 
 
 540 280 
 
 5 426 
 
 3 277 
 
 1 
 
 180 
 
 8 242 
 
 42 
 
 113 550 
 
 1 847 003 
 
 421 360 
 
 5 181 
 
 3 078 
 
 
 920 
 
 8 234 
 
 43 
 
 108 110 
 
 1 733 453 
 
 307 810 
 
 4 933 
 
 2 889 
 
 
 672 
 
 8 223 
 
 44 
 
 102 620 
 
 1 625 343 
 
 199 700 
 
 4 683 
 
 2 709 
 
 
 436 
 
 8 209 
 
 45 
 
 97 080. 
 
 1 522 723 
 
 97 080 
 
 4 430 
 
 2 538 
 
 
 212 
 
 8 190 
 
 46 
 
 91 480 
 
 1 425 643 
 
 
 4 174 
 
 2 376 
 
 
 
 8 165 
 
 47 
 
 •85 830 
 
 1 334 163 
 
 
 3 916 
 
 2 224 
 
 
 
 8 136 
 
 48 
 
 80 130 
 
 1 248 333 
 
 
 3 656 
 
 2 081 
 
 
 
 8 099 
 
 49 
 
 74 400 
 
 1 168 203 
 
 
 3 394 
 
 1 947 
 
 
 
 8 055 
 
 50 
 
 68 640 
 
 1 093 803 
 
 
 3 130 
 
 1 823 
 
 
 
 8 001 
 
36 AGES OF VOLUNTEERS. 
 
 The results present some curious contrasts between the life- 
 curves for the total population in the loyal States and in the 
 insurgent States, which may be best recognized by reference to 
 the appended chart, marked E. This chart exhibits the number 
 of white males at each year of age from 18 to 50, corresponding 
 to each 10 000 at the age of 18. It will be seen at once that the 
 curvature of the line representing the population of the insurgent 
 States is in the direction opposite to that of the lines belonging 
 to the loyal States and to the whole country. The dotted line 
 is straight, and shows what the distribution would be, did it follow 
 a regular arithmetical progression. To what extent this differ- 
 ence may be due to immigration from Europe, which has been 
 chiefly to the Free States, I will not undertake to estimate. We 
 have seen, however, that the law of distribution of our volunteer 
 troops according to ages was essentially the same for those States 
 to which immigration is ■ greatest as for those to which it is 
 least. 
 
 The construction of all the curves laid down on the accompany- 
 ing charts will be manifest without explanation. For those or- 
 dinates which belong to the respective ages they give the corre- 
 sponding numbers. 
 
APPENDIX. 
 
 ON THE AGES OF A POPULATION. 
 
 In the course of the preceding investigation, the interesting question as 
 to the general distribution of a population by ages became prominent ; and 
 the inquiry continually suggested itself, how far any simple formula might 
 be capable of representing the observed numbers for all ages of life. This 
 has incidentally led to the detection of what seems to be the true law, which, 
 although not strictly pertaining to the subject in hand, seems yet to possess 
 sufficient practical value and importance in its indirect bearing to justify its 
 introduction here, — the more especially, since endeavors to obtain informa- 
 tion on this point elsewhere have proved fruitless. 
 
 It appears that, in a population at all homogeneous in its character, the 
 number of persons under the age n years may be represented by the simple 
 expression 
 
 N= a sin n k n 6 
 
 in which a denotes the total number of the population, while k and 6 are 
 constants peculiar to the country and epoch. The quantity 6 is an angle 
 somewhat larger than 1°, and k is a number, generally a little less than 
 unity. 
 
 For the special case &= 1, the formula becomes 
 
 iV= a sin n 8 
 
 containing only one unknown quantity, the angle 6, to be determined by 
 investigation. 
 
 A very peculiar characteristic of this law is recognizable in the circum- 
 stance that the number at any given age appears to be strictly proportional 
 to the whole population ; so that the expectation of life, for the average indi- 
 vidual, is as well represented as is the general distribution by ages of the 
 total number of individuals, of whom the population is composed. 
 
38 AGES OF VOLUNTEERS. 
 
 Investigating the values of the constants k and 6 for the people of the 
 United States at each of the last four enumerations, we find 
 
 Date k 6 
 
 1830 0.9918 2°.0524 
 
 1840 0.9921 1°.9747 
 
 1850 0.9932 1°.8361 
 
 1860 0.9941 1°.7307. 
 
 The census of 1820 is not sufficiently distinct, in the assortment by ages, 
 to permit a determination of the constants, but the indications are clear 
 that a proper enumeration would have afforded results in conformity with 
 the preceding series ; the value of k being smaller, and that of 6 larger than 
 for the population in 1830. 
 
 The curious fact thus becomes evident, that our population has, during 
 the last forty years or more, been gradually assimilating itself to the normal 
 type represented by k = 1 ; growing, or developing itself, so to speak, 
 toward a compliance with the simple law 
 
 iV= a sin n 6 
 
 in which the value of 6 indicates the longevity of the people, since, accord- 
 ing to the formula, the entire population becomes extinct at the age when 
 nd=90°. 
 
 How far immigration has affected the values of the constants for the 
 United States we will not now inquire. Were the tendency to immigrate 
 independent of age, no appreciable influence could be traced to this source ; 
 and the character of the immigration into this country seems to have been 
 such as to exhibit no great preponderance or deficiency for any one period of 
 life, except perhaps that there is some deficiency in the relative number at 
 the most advanced ages. But the accessions to our population from Ireland 
 and Germany appear to have been in most cases by families, and not com- 
 posed chiefly of persons in the prime of life or fullness of strength, as is the 
 case in very new countries. 
 
 The English people appearing to afford a fair specimen of a permanent 
 and normal population, the last two censuses of England and Wales were 
 examined, and with the following result : — 
 
 Date 
 
 k 
 
 6 
 
 1851 
 
 0.9957 
 
 1°.4702 
 
 1861 
 
 0.9962 
 
 1°.4316. 
 
 Thus a similar phenomenon is manifested by the English enumeratibns to 
 that exhibited by the American census-returns ; the values of k approach- 
 ing unity, and those of 6 diminishing. The smaller value of the angle 6 
 
AGES OF VOLUNTEERS. 39 
 
 indicates a longer duration of life in that country ; but k, the modulus of 
 the change by geometric progression, was not larger for England in 1851 
 than it bids fair to be for the United States in ten years from the present 
 time. 
 
 Passing next to the French population, we find the value k = 1 as the 
 result alike of the last three enumerations, the values of 6 being 
 
 in 1851 
 
 1°.0553 
 
 " 1856 
 
 1°.0556 
 
 " 1861 
 
 1°.0473. 
 
 The remarkable peculiarity of the life-curve for France, as regards the 
 small infantile mortality, is well exhibited by the chart F, which shows 
 the number living, at,each year of age, for every million in the population. 
 The several curves of this chart represent the distribution of ages for the 
 United States in 1830 and 1860, (those for the intermediate decades being 
 omitted to avoid confusion,) for England in 1861, and for France. The 
 English curve for 1851 would differ too slightly from that for 1861 to be 
 conveniently distinguished on the chart; and the French curves for 1851, 
 1856, and 1861 would be undistinguishable from one another. 
 
 The chart G shows the corresponding values of N, (the number under 
 each year of age,) for each nation, and clearly manifests the differences in 
 the law, corresponding to the diversity in the constants. 
 
 The tables of population deduced from the census-returns already cited, 
 together with the values given by the formula, are here appended, reduced 
 however, in each case, to the scale of one million of population. The dif- 
 ferences are given in decimals of the census-numbers, and the accordance 
 between the formula and the recorded numbers will be manifest at the first 
 inspection. The chief discrepancies will be found in the French tables, for 
 the ages 
 
 exceeding 50, in the census of 1851 
 « 55, " " " " 1856 
 " 60, " " " " 1861. 
 
 This curious circumstance and the nature of the discordances suggest some 
 historical explanation ; which the disturbed condition of the French nation 
 at the period corresponding to the birth of this portion of the population 
 seems to render plausible. 
 
40 
 
 AGES OF VOLUNTEERS. 
 
 TABLE XXII. 
 
 Ages of the Population of the United States, 
 as deduced from the Census Returns of 1830 and 1840. 
 
 AGE. 
 
 Census of 1830. 
 
 Census of 1840. 
 
 Proportions 
 Observed. 
 
 tl numbers. 
 Calculated. 
 
 Difference. 
 (C.-O.) 
 
 Proportion 
 Observed. 
 
 il numbers. 
 Calculated. 
 
 Difference. 
 (C-O.) 
 
 0- 5 
 
 17977 
 
 17082 
 
 -0.050 
 
 17437 
 
 16334 
 
 -0.063 
 
 5-10 
 
 14576 
 
 15254 
 
 +0.046 
 
 14173 
 
 14651 
 
 +0.034 
 
 10- 15 
 
 12452 
 
 13280 
 
 +0.014 
 
 12094 
 
 12931 
 
 +0.069 
 
 15 - 20 
 
 11147 
 
 11318 
 
 +0.024 
 
 10911 
 
 11205 
 
 +0-027 
 
 20-30 
 
 17752 
 
 17244 
 
 -0.029 
 
 18155 
 
 17456 
 
 -0.038 
 
 30-40 
 
 10908 
 
 11287 
 
 +0.035 
 
 11597 
 
 11790 
 
 +0.017 
 
 40 - 50 
 
 6886 
 
 6932 
 
 +0.007 
 
 7320 
 
 7466 
 
 +0.020 
 
 50-60 
 
 4308 
 
 3973 
 
 -0.078 
 
 4365 
 
 4389 
 
 +0.005 
 
 60-70 
 
 2525 
 
 2100 
 
 -0.168 
 
 2449 
 
 2343 
 
 -0.043 
 
 70-80 
 
 1104 
 
 992 
 
 -0.100 
 
 1132 
 
 1067 
 
 -0.058 
 
 80 & over 
 
 365 
 
 540 
 
 
 367 
 
 368 
 
 
 TABLE XXIII. 
 
 Ages of the Population of the United States, 
 as deduced from the Census Returns of 1850 and 1860. 
 
 AGE. 
 
 Census of 1850. 
 
 Census of 1860. 
 
 Proportion; 
 Observed. 
 
 il numbers. 
 Calculated. 
 
 Difference. 
 (C.-O.) 
 
 Proportion) 
 Observed. 
 
 il numbers. 
 Calculated. 
 
 Difference. 
 (C.-O.) 
 
 0- 1 
 
 2751 
 
 3170 
 
 +0.152 
 
 2998 
 
 3003 
 
 +0.002 
 
 1-5 
 
 12070 
 
 12215 
 
 +0.012 
 
 12300 
 
 11608 
 
 -0.056 
 
 5-10 
 
 13836 
 
 14102 
 
 +0.019 
 
 13117 
 
 13484 
 
 +0.028 
 
 10- 15 
 
 12292 
 
 12564 
 
 +0.022 
 
 11588 
 
 12206 
 
 +0.053 
 
 15-20 
 
 10892 
 
 10990 
 
 +0.009 
 
 10625 
 
 10853 
 
 +0.021 
 
 20-30 
 
 18562 
 
 17505 
 
 -0.057 
 
 18242 
 
 17692 
 
 -0.030 
 
 30-40 
 
 12368 
 
 12225 
 
 -0.012 
 
 13012 
 
 12760 
 
 -0.019 
 
 40-50 
 
 8130 
 
 8019 
 
 -0.013 
 
 8496 
 
 8618 
 
 +0.014 
 
 50-60 
 
 4903 
 
 4883 
 
 -0.041 
 
 5214 
 
 5366 
 
 +0.029 
 
 60-70 
 
 2667 
 
 2695 
 
 +0.010 
 
 2910 
 
 2953 
 
 +0.015 
 
 70-80 
 
 1147 
 
 1250 
 
 +0.090 
 
 1158 
 
 1261 
 
 +0.089 
 
 80 & over 
 
 382 
 
 382 
 
 
 340 
 
 196 
 
 
AGES OF VOLUNTEERS. 
 
 41 
 
 TABLE XXIV. 
 
 Ages of the Population of England and Wales, 
 as deduced from the Census Returns of 1851 and 1861. 
 
 AGE. 
 
 Census of 1851. 
 
 Census of 1861. 
 
 Proportion 
 Observed 
 
 il numbers. 
 Calculated. 
 
 Difference. 
 (C. - O.) 
 
 Proportion! 
 Observed. 
 
 il numbers. 
 Calculated. 
 
 Difference. 
 (C. - O.) 
 
 0- 5 
 
 13006 
 
 12533 
 
 -0.035 
 
 13352 
 
 12245 
 
 -0.083 
 
 5-10 
 
 11590 
 
 11800 
 
 +0.018 
 
 11588 
 
 11575 
 
 -0.001 
 
 10-15 
 
 10616 
 
 10987 
 
 +0.034 
 
 10415 
 
 10819 
 
 +0.040 
 
 15-20 
 
 9832 
 
 10079 
 
 +0.013 
 
 9688 
 
 10007 
 
 +0.032 
 
 20-25 
 
 9441 
 
 9114 
 
 -0.036 
 
 9317 
 
 9108 
 
 -0.023 
 
 25-30 
 
 8307 
 
 8170 
 
 -0.017 
 
 7932 
 
 8178 
 
 +0.030 
 
 30-35 
 
 7168 
 
 7179 
 
 +0.004 
 
 6950 
 
 7282 
 
 +0.046 
 
 35-40 
 
 6083 
 
 7273 
 
 +0.030 
 
 6111 
 
 6352 
 
 +0.038 
 
 40-45 
 
 5393 
 
 5378 
 
 -0.003 
 
 5638 
 
 5506 
 
 -0.024 
 
 45-50 
 
 4440 
 
 4546 
 
 +0.023 
 
 4617 
 
 4705 
 
 +0.019 
 
 50-55 
 
 3934 
 
 '3782 
 
 -0.040 
 
 3995 
 
 3820 
 
 -0.046 
 
 55-60 
 
 2919 
 
 3061 
 
 +0.046 
 
 3039 
 
 3245 
 
 +0.063 
 
 60-65 
 
 2668 
 
 2426 
 
 -0.100 
 
 2751 
 
 2512 
 
 -0.095 
 
 65-70 
 
 1815 
 
 1841 
 
 +0.014 
 
 1862 
 
 1910 
 
 +0.025 
 
 70-75 
 
 1386 
 
 1332 
 
 -0.041 
 
 1391 
 
 1355 
 
 -0.026 
 
 75-80 
 
 809 
 
 876 
 
 +0.076 
 
 794 
 
 869 
 
 +0.086 
 
 80-85 
 
 410 
 
 481 
 
 +0.173 
 
 394 
 
 435 
 
 +0.104 
 
 85 & over. 
 
 183 
 
 142 
 
 
 146 
 
 77 
 
 
 Total, 
 
 100000 
 
 100000 
 
 
 100000 
 
 100000 
 
 
 FORMULAS 
 
 For 1851, JST= 100 000 sin n (0.99575)" . 1°.4702. 
 1861, IT= 100 000 sin n (0.99616)" . 1°.4316. 
 
 6 
 
42 
 
 AGES OF VOLUNTEERS. 
 
 TABLE XXV. 
 
 Ages of the Population of France, 
 as deduced from the Census Returns of 1851, 1856, and 1861. 
 
 AGE. 
 
 0- 
 5- 
 10- 
 15- 
 20- 
 25- 
 30- 
 35- 
 40- 
 45- 
 50- 
 55- 
 60- 
 65 
 70- 
 75 
 80 
 85 J 
 
 5 
 
 10 
 15 
 20 
 25 
 •30 
 35 
 
 ■ 10 
 45 
 
 ■ 50 
 
 ■ 55 
 ■60 
 •65 
 -70 
 -75 
 -80 
 -85 
 
 i over. 
 
 Census of 1851. 
 
 Proportional 
 numbers. 
 
 Ob- Caleu- 
 served. lated. 
 
 Total, 
 
 9291 
 9216 
 8800 
 8805 
 8326 
 8020 
 7565 
 7188 
 6596 
 5S69 
 5782 
 4390 
 3670 
 2785 
 1952 
 1062 
 480 
 203 
 
 100000 
 
 Difference. 
 (C.-O.) 
 
 9208 
 9130 
 8946 
 8716 
 8437 
 8036 
 7616 
 7105 
 6534 
 5890 
 5233 
 4512 
 3753 
 2954 
 2148 
 1313 
 468 
 1 
 
 100000 
 
 -0.009 
 -0.009 
 +0.016 
 -0.010 
 +0.013 
 +0.002 
 +0.007 
 -0.012 
 -0.009 
 +0.004 
 -0.095 
 +0.028 
 +0.023 
 +0.059 
 +0.100 
 +0.239 
 -0.025 
 
 Census of 1856. 
 
 Proportional 
 numbers. 
 
 Ob- 
 served. 
 
 9568 
 9120 
 8821 
 8530 
 8077 
 8075 
 7575 
 7255 
 6656 
 6041 
 5317 
 4838 
 3734 
 2757 
 1902 
 1088 
 453 
 193 
 
 100000 
 
 Calcu- 
 lated. 
 
 Difference. 
 (C - O.) 
 
 9200 
 9119 
 8965 
 8736 
 8427 
 8051 
 7614 
 7092 
 6526 
 5902 
 5228 
 4503 
 3753 
 2958 
 2145 
 1312 
 468 
 1 
 
 100000 
 
 -0.038 
 0.000 
 +0.016 
 +0.024 
 +0.043 
 -0.003 
 +0.005 
 -0.022 
 -0.020 
 -0.023 
 -0.017 
 -0.069 
 +0.005 
 +0.076 
 +0.128 
 +0.205 
 -0.033 
 
 Census of 1861. 
 
 Proportional 
 numbers. 
 
 Ob- Calcu- 
 
 served. lated. 
 
 9677 
 8767 
 8668 
 8701 
 8237 
 7857 
 7421 
 7098 
 6625 
 6155 
 5382 
 4559 
 4160 
 2941 
 1940 
 1123 
 490 
 199 
 
 100000 
 
 Difference. 
 (0. - 0.) 
 
 9124 
 9052 
 8898 
 8722 
 8374 
 8005 
 7564 
 7071 
 6514 
 5900 
 5254 
 4518 
 3790 
 3016 
 2218 
 1398 
 568 
 14 
 
 100000 
 
 -0.088 
 +0.032 
 +0.027 
 +0.002 
 +0.017 
 +0.019 
 +0.019 
 -0.004 
 -0.017 
 -0.041 
 -0.024 
 -0.009 
 -0.090 
 +0.025 
 +0.143 
 +0.245 
 +0.159 
 
 FORMULAS 
 
 For 1851, N= 100 000 sin n (1°.0553). 
 1856, N= 100 000 sin n (1°.0556). 
 1861, N= 100 000 sin n (1°.0473). 
 
AGES OF VOLUNTEERS. 43 
 
 The agreement of the observed numbers with those given by our formula 
 is indicated by the quantities in the columns headed G. — 0. (i. e. Com- 
 puted minus Observed), and appears to be entirely within the limits of 
 probable error in the enumeration, — if we except those discordances for 
 the French census already alluded to. It affords a strong argument for 
 belief that the true form of the normal life-curve is closely represented 
 by the sine-formula. 
 
 The only other statistics of ages for European populations, which have 
 been conveniently accessible, are contained in the abstract of the Prussian 
 census of 1852, given by Brachelli, in the second volume of his Deutsche 
 Staatenkunde. A discussion of the numbers there recorded gives 
 
 jfe = 0.9960, 0=1°.47O2, 
 
 these values being closely similar to those for England and Wales in 
 1851. 
 
 It is manifest that if the number under any given age n be represented 
 by the expression 
 
 N = a sin n k 71 8 
 
 the number between the ages n and n-\-\ will be expressed by 
 
 2a sin ^kf 1 (kn-\-k — n)6. cos ^k 71 (k n -\- k -{- n) 6, 
 
 and the mortality at the same period, by the finite difference of this quantity. 
 But when 6 becomes unity, these values are greatly simplified, and we 
 have 
 
 Population under the age n years = a sin n 6 
 
 Population at " " " " = 2a sin \6 cos (n-\- ±)d 
 
 Mortality " " « " " = 4 a sin (n + 1) 6 sin 2 \6. 
 
 According to the formula here presented, the life-curve for advanced ages 
 bears no similarity to an asymptote, but ceases abruptly when the quantity 
 
 90° 
 n k"6 = 90° ; or for the case of k = 1, when n = - . This indicates that 
 
 8 
 
 all ages above this limit are exceptional, and to be regarded in the same 
 light as deviations from the theoretical number at other periods of life. 
 
 The many paths of research offered by the residual discordances from 
 the formula must be passed by on this occasion, with the single remark that 
 they offer indications of abundant reward for any explorer. 
 
 It is proper to add, that in these investigations, as in those on the Ages of 
 Volunteers, the computations have been almost exclusively carried on by 
 Mr. J. N. Stockwell. 
 
 Cambridge, January, 1866. 
 
Thonsi 
 
 ^frUt A. 
 
 *i //f'ftrf//'f/(/r f/te /'( /<///<>// 
 
 z Jed and/wmputed namdc/w. 
 
 represent the recorded numbers i 
 ■>l(? are computed. Those for officers 
 i, for greater distinctness. ) 
 
 22< 
 
 •ion 
 
 IM 
 
 IttO 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 140 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 G&O 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 I«KI 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 SO 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 <)() 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 K» 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 20 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 - 
 
 
 
 
 
 
 
 
 
 
 r === 
 
 -:- 
 
 
 
 
 
 \.$e, IS 
 
 + 
 
 » + 
 
 i 
 
 + 
 
 ■» t 
 
 i 4 
 
 + 
 
 S 
 
 t- 
 
 Years. 
 
Chant Ji. 
 
 Exhibiting fortach year #f age f/te relation 
 oetmxn the recorded andjcomputed numbers, 
 of volunteers. 
 
 (The dotted lines represenl the recorded numbers) 
 Ulp contimioua oneg are computed. Those for officers 
 are multiplied by ten, for greater distinctness.) 
 
 Ave. ik |,q 20 ii i'i 23 2* ' i6 2<i 
 
 2« T. M 
 
 ).) 30 31 32 33 34 35 36 .17 38 
 
 39 40 +t te +•> ** H S6 
 
 17 W 10 V»'.l 
 
Xiimlifi 
 
 10,00(1 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 \ 
 
 9.000 
 
 
 
 
 
 
 
 
 
 
 
 A 
 
 
 
 
 \ 
 
 
 
 
 
 
 ,S.O(ll> 
 
 
 
 
 
 
 
 
 
 
 
 
 V 
 
 
 
 
 
 v., 
 
 
 
 
 
 \\ 
 
 
 7.UIIO 
 
 
 
 
 
 
 
 
 
 
 
 
 
 K 
 
 
 
 
 
 \\ 
 
 OOOO 
 
 
 
 
 \^, 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 5,000 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 tpoo 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .'l.itOO 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Age 18 l!» 20 „'i 2 
 
XiiiiiImT 
 
 10,0 CM 
 
 
 
 
 
 >r,. 
 
 
 
 
 
 
 L/iart //. 
 
 
 
 
 
 
 
 
 
 
 
 
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 , 
 
 population of mi/ifari/ /?///> ,//„>„/ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 Y 
 
 
 
 
 
 
 
 
 
 
 
 <- 
 
 
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 8,000 
 
 
 
 
 
 1 1111 ii.M.r.i lilies IIKMCIle MIC ITCOnlCd IIHIIllXTS 
 
 
 
 
 
 
 
 
 
 £5, 
 
 
 
 the continuous lilies thiToiiiuiiteil ones.) 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 \\ 
 
 
 
 
 
 
 
 
 
 
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 - 
 
 
 
 
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 tDOO 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 V^r 
 
 
 
 
 
 
 
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 \^s 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 s^jfe 
 
 
 
 
 
 
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 'sT 
 
 
 
 
 
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 Lz 
 
 
 
 
 
 J_J 
 
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 1 
 
 
 
 
 1 
 
 
 
 1 1 1 1 1 1 
 
 Age 18 19 20 ii 22 23 24 25 26 27 28 29 30 
 
 31 .12 33 ;<4 35 36 37 38 if) -to U 42 -f;i 44 (.'. Yearn 
 
Number 
 
 
 
 
 
 
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 ^: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 _Jl 
 
 
 
 
 
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1000 
 
 aooo 
 
 2,000 
 
 CAart C 
 
 ExkiditingJbreacA year of age tAenum- 
 bn •»/ >//// ?ted men and officers among Mr 
 first million i vlnnteers, and ihe number 
 o/t i hilt males in ^population WWi/offhr 
 / hi ted . S Votes andqftAe loyal ■ S inte »-. 
 
 The doited lines are straight. The number 
 of officers is multiplied by ten for distinctness. 
 
 M<~ W 19 20 21 22 23 2* 25 26 27 28 2? 
 
 .11 32 ;5.'l 3# 3* ;J6 •' 17 ;,H ~'> *° M K 13 ^ M ffl W *fl W ■'>•• Ve.'i* 
 
Numbej 
 10,000 
 
 •1000 
 
 80(10 
 
 7001) 
 
 ('hurt /). 
 ShoH /'//{/ /or ////// r.sf > vhtatfn x. the n///o of 
 tffieexs&mtn /»//// n -hifc male populatwn 
 qfithe loyal states at the same ages. 
 • (Thenumber of officers is multiplied byten.) 
 
 toon 
 
 aooo 
 
 lOOO 
 
 A§e 18 ; li 20 21 22 83 2* 25 2« 27 28 2!) .10 31 32 33 34 
 
 3,5 .16 37 -IK 38 Wi H VI 43 44 f"> Yc.ir.s. 
 
Number 
 
 10,000 
 
 
 
 
 
 
 
 
 J^5 
 
 ^> 
 
 ;— 
 
 
 
 
 
 
 9,000 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 8,000 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 r.iiiio 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 6000 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 5,000 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 4,000 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .1,000 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 2,000 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 L0O0 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Aye 18 19 20 21 
 
; 
 
 Number 
 
 10,000 
 
 
 
 
 
 /'/,., ,-t /<' 
 
 
 -S 
 
 
 
 
 
 
 — - 
 
 
 
 
 
 
 9,000 
 
 r^ 
 
 
 "^ 
 
 4 
 
 ^ 
 
 
 
 H'/tifr ////■///■ population o/'//h United' 
 •States, Loyal States A'- IhsuryrentStates. 
 
 
 
 
 
 
 
 
 i^a 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 "& 
 
 
 
 
 
 
 
 
 
 ~- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 \*& 
 
 
 
 8,000 
 
 
 
 
 
 
 
 
 
 
 
 *s-- 
 
 ^ 
 
 t* i • 
 
 
 
 
 
 
 
 
 
 
 
 
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 t r 'i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^4 
 
 » * 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 : 
 
 
 v* 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 ■o, 
 
 
 
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 v, 
 
 
 
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 siy 
 
 •// 
 
 
 
 *-, 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 5& 
 
 i» 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 4,000 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .1,000 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 2,000 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 4- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 . 
 
 Age lfi 10 20 21 ZZ 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 to 40 W 48 49 r >() Y.-ars. 
 
Number 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 to.OOO 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 \ \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 35,000 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 s 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ,'JO.OOO 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 - 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 35.000 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 30.000 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 i i r 
 
 5,000 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 - 
 
 
 -4-4 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 — & 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Aye 
 
 80 <s. r > 00 Yea 
 
Chart F. 
 
 Showing tfte distribution qfct million of population, 
 
 //// //ror.s- ofi'f/c Jbrt/tr United States, England, & France. 
 


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 10,000 - 
 9,000 - 
 8,000 - 
 
 7, (ion - 
 
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 CAart & 
 
 Exhibiting the reiativie numder of dhe population under 
 
 each succefsii v yea/ ■o/'a//c,Jb/'/ltr / r //i//ri . ftates, JEngland, durance. 
 
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