FIG. 3. Age specific death rate from Penumonia (all forms) in Pittsburgh,

Pa., during the period 1900-1920.

It is noticeable that the population of Pittsburgh is growing older, the percentages in the distribution decreasing below and increasing above an age

FIG. 4. Age specific death rate from Pneumonia (all forms) in the Ten Original Registration States, during the period 1900-1920.

NOTE. In the tables for the specific death rates the numbers are carried to one decimal place as is often the case; but the number of significant figures is variable. If N is the population and n the number of deaths, the rate p is n/N. The fluctuation of sampling for the number n is V(Npq) where q=1p is approximately 1, so that approximately the fluctuation is V (Np)=√n. The fluctuation in the rate is V (pq/N), approximately V (p/N). As the rate p is given in hundreds of thousands, the population should be measured in hundreds of thousands. Thus in 1900 the population of age 0-4 is 51,000 and N = 1/2 in hundreds of thousands; the fluctuation in Þ expressed as 649.6 per hundred thousand is V (650/0.5) = V 1,300 = 36. We should therefore write 650 ± 36. In like manner in the group 70-up in 1900 we find N.06 and the fluctuation is V (993/.06) = V 16,200 127 and the rate should be-written 993 ± 127. On the other hand for the group 20-29 in 1900, N = .99 and V (64.5/.99) V65.1 = 8.1 and the rate is 64.5±8.1. Thus

of about 40 years. Various refinements could have been applied in estimating the population in the different age groups in intercensal years in place of the crude method of arithmetic interpolation, but they seemed hardly worth

TABLE II.

AGE SPECIFIC DEATH RATE PER 100,000 POPULATION IN PITTSBURGH, 1900-1920.

40-49.

50-59.

60-69.

70 up.

120.0 232.5 235.8 267.4 327.5 449.0 542.0 520.0 827.0 957.0 1042.0 614.0 1002.0 .1275.0 1687.0 2090.0 2580.0 1777.0 2500.0 2074.0

280.6 165.6

257.0

279.7

353.4 412.2

473.2

897.2

20-29.

54.5

160.4

933.2

194.2

164.9

30-39.

134.7

40-49

50-59.

452.0

489.c

60-69.

70 up.

72.5 130.3 131.6 219.0 226.5 410.6 890.0 327.0 447.0 470.0 630.0 682.9 905.0 800.0 812.0 1198.0 949.0 1320.0 808.0 978.0 .2006.0 2132.0 2580.0 2467.0 2190.0 2126.0 2396.0

although the rates 2,126.0 and 2,396.0 for 1919 and 1920 in the age group 70– up look very different each is subject to a standard deviation of sampling of about 145, their difference 270 is subject to a fluctuation of about 200 and possesses no very great statistical significance. It would be more rational and more convenient to suppress the non-significant figures and round the numbers off, but as this procedure is not widespread in vital statistics we leave the figures as they stand. It should be remembered that few of the rates are good to 5 per cent. and many of them are not good to 10 per cent. Calculations such as these can safely be made with a 20-inch slide rule or even with a 10-inch rule and many of them throughout this paper have been so made. So much for fluctuations of simple sampling. The figures of the local authorities and of the federal authorities differ one from another, sometimes markedly, and even the federal figures printed in one and the same volume

FIG. 5. Age specific death rate from Broncho-pneumonia in Pittsburgh, Pa., during the period 1900-1920.

will differ-e.g., the crude death rate from pneumonia, all forms, in Pittsburgh in 1920 is given in "U. S. Mortality Rates, 1910-1920," as 342.8 on pp. 19, 110, 586 and as 341.3 on pp. 108, 287.

III. DISCUSSION OF THE TREND.

8. From the figures for the age specific death rates per hundred thousand the yearly trend for the period 1900-1920 has been com

30-39.

15.7

15.6

40-49.

39.0

50-59.

60-69.

70 on.

18.7 34.8 26.5 39.0 32.6 103.0 91.0 102.0 114.0 85.9 138.0 277.0 200.0 334.0 269.0 280.0 303.0 313.0 816.0 1060.0 1080.0 922.0 760.0 1156.0 1096.0

126.0

43.2

49.7

64.0

65.7

108.0 127.0

puted (Table III.), in most cases both with the abnormal influenza year and without it. The trends with 1918 excluded are probably more significant. It is noticeable that bronchopneumonia and pneumonia, all forms, are increasing at all ages and that lobar and undefined pneumonia is increasing in all age groups other than infancy and 0-4. It should be emphasized that these figures have naturally to do only with the reported statistics and not necessarily with actual pneumonia. As the rates in the different age groups differ so much it is illuminating to compare the rate of yearly increase with the mean.

Compare with Fig. 4 which shows that for the ten original registrative states the pneumonia mortality is sensibly stationary in all age groups.