Hints from the Health Department. Leaflet from the archive of the Society of Medical Officers of Health. Credit: Wellcome Collection, London
Thirty-eighth annual report of the Vestry...
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Table—Showing Mean duration of Life under different conditions of the Birth-rate and Death-rate.
Annual variation of population
per cent.
Death-rate 5 per cent.
Death-rate 1 per cent.
Death-rate 1.5 per cent.
Death-rate 2 per cent.
Death-rate 2.5 per cent.
Death-rate 3 per cent.
Death-rate 3.5 per cent.
Death-rate 4 per cent.
Birth-rate
per cent.
Mean duration
of life.
Birth-rate
per cent.
Mean duration
of life.
Mean duration
of life.
Birth-rate
per cent.
Mean duration
of life.
Birth-rate
per cent.
Mean duration
of life.
Birth-rate
per cent.
Mean duration
of life.
Birth-rate
per cent.
Mean duration
of life.
Birth-:ate
per cent.
Birth rate
per cent.
Mean duration
of life.
7.6
101
6.66
101.5
6.08
102
5.67
103
5.10
103.5
4.89
104
4.70
Increasing 100
100.5
102.5
5.35
10.5
11
11.5
13
14
21.37
12
12.5
13.5
„ 10
31.9
25.16
18.80
16.88
15.38
14.16
13.14
8.5
11.5
12
14.28
36.81
28.55
9.5
23.98
10
20.91
10.5
11
„ 8
9
18.65
16.88
15.46
36.72
7.5
8
5.5
6
6.5
30.05
25.67
8.5
16.62
7
22.52
20.10
18.19
9
„ 5
49.15
38.73
7.5
8
52.31
5.5
6
31.49
6.5
26.78
7
8.5
17.12
5
23.39
20.82
18.78
4.5
24.36
7
56.02
41.03
6
28.02
6.5
21.60
7.5
„ 4
4.5
5.5
33.14
19.43
8
17.67
5
43.72
29.41
6.5
7
4
4.5
5
34.91
6
7.5
18.27
„ 3.5
60.4
5.5
25.45
22.47
20.15
65.8
6.5
46.90
37.16
30.99
5.5
6
7
18.93
„ 3
4
4.5
5
20.67
23.45
20.94
3.5
4
3
72.56
3.5
50.73
39.74
28.07
6
6.5
19.66
„ 2.5
4.5
32.85
5
5.5
24.54
21.83
81.27
3
55.48
3.5
4
4.5
5
5.5
6
20.47
2
2.5
42.78
35.00
29.68
22.82
25.80
2.5
61.54
3
4
93-1
3.5
4.5
27.23
5
5.5
21.39
„ 1.5
2
46.55
37.28
31.56
23.96
110.4
2
69.66
51.34
3
40.75
4.5
5
„ 1
1.5
2.5
3.5
33.82
28.91
25.26
22.43
4
2.5
3
4.5
„ 0.5
138.98
2
44.75
3.5
23.61
1.5
81.30
57.67
36.55
4
26.77
1
30.91
1.5
66.66
200
100
50
2.5
40
3
Stationary 0
1
2
33.33
3.5
4
25
0.5
28.57
...
...
Diminishing — 0.45
510.54
...
...
...
...
...
...
...
...
...
...
0.05
...
...
2
„ -0.5
1
80.89
1.5
2.5
0
138.28
57.39
44.52
36.37
3
30.75
3.5
26.64
8
0.5
...
...
„ -0.95
0.05
...
...
...
...
...
...
313.84
...
...
...
...
...
...
68.97
40.34
„ - 1
0
0.5
1
1.5
2
3
28.62
...
8
109.31
50.93
2.5
33.48
...
...
...
„ - 1.45
...
...
...
...
...
...
0.05
232.86
...
...
...
...
...
2
...
...
0.5
1
60.63
45.86
„ -1.5
...
...
0
91.72
1.5
2.5
8
37.03
31.10
...
...
„ -195
...
0.05
187.32
...
...
...
b=birth-rate of one unit for one year
...
...
...
...
...
0
54.38
1.5
2
34.31
d=death-rate „ „
0.5
79.66
1
41.94
„ -2
8
1.5
...
...
...
...
-2.45
r=inerease „ „ =b—a
...
0.05
157.71
...
...
...
0.5
1
x=number of years, or mean duration of life
0
38.74
„ - 2.5
...
...
8
70.77
49.47
1.5
...
...
0.05
136.73
...
...
„ -2.95
(1+r)x=b/d
log. b/d
x=
log.(1+r)
...
...
...
...
0
...
...
0.5
45.52
„ -3
...
63.89
1
...
8
...
...
...
...
...
...
„ — 3.45
...
...
...
0.05
...
121.01
...
...
„ —3.5
...
...
...
0
0.5
58.37
8
...
...
...
...
...
„ —3.95
...
...
...
...
0.05
108.73
-
...
...
...
...
...
...
...
...
0
...
Table—Showing Mean duration of Life under different conditions of the Birth-rate and Death-rate.
Annual variation of population per cent. | Death-rate 5 per cent. | Death-rate 1 per cent. | Death-rate 1.5 per cent. | Death-rate 2 per cent. | Death-rate 2.5 per cent. | Death-rate 3 per cent. | Death-rate 3.5 per cent. | Death-rate 4 per cent. | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Birth-rate per cent. | Mean duration of life. | Birth-rate per cent. | Mean duration of life. | Birth-rate per cent. | Mean duration of life. | Birth-rate per cent. | Mean duration of life. | Birth-rate per cent. | Mean duration of life. | Birth-rate per cent. | Mean duration of life. | Birth-:ate per cent. | Mean duration of life. | Birth rate per cent. | Mean duration of life. | |
Increasing 100 | 100.5 | 7.6 | 101 | 6.66 | 101.5 | 6.08 | 102 | 5.67 | 102.5 | 5.35 | 103 | 5.10 | 103.5 | 4.89 | 104 | 4.70 |
„ 10 | 10.5 | 31.9 | 11 | 25.16 | 11.5 | 21.37 | 12 | 18.80 | 12.5 | 16.88 | 13 | 15.38 | 13.5 | 14.16 | 14 | 13.14 |
„ 8 | 8.5 | 36.81 | 9 | 28.55 | 9.5 | 23.98 | 10 | 20.91 | 10.5 | 18.65 | 11 | 16.88 | 11.5 | 15.46 | 12 | 14.28 |
„ 5 | 5.5 | 49.15 | 6 | 36.72 | 6.5 | 30.05 | 7 | 25.67 | 7.5 | 22.52 | 8 | 20.10 | 8.5 | 18.19 | 9 | 16.62 |
4.5 | 5 | 52.31 | 5.5 | 38.73 | 6 | 31.49 | 6.5 | 26.78 | 7 | 23.39 | 7.5 | 20.82 | 8 | 18.78 | 8.5 | 17.12 |
„ 4 | 4.5 | 56.02 | 5 | 41.03 | 5.5 | 33.14 | 6 | 28.02 | 6.5 | 24.36 | 7 | 21.60 | 7.5 | 19.43 | 8 | 17.67 |
„ 3.5 | 4 | 60.4 | 4.5 | 43.72 | 5 | 34.91 | 5.5 | 29.41 | 6 | 25.45 | 6.5 | 22.47 | 7 | 20.15 | 7.5 | 18.27 |
„ 3 | 3.5 | 65.8 | 4 | 46.90 | 4.5 | 37.16 | 5 | 30.99 | 5.5 | 26.67 | 6 | 23.45 | 6.5 | 20.94 | 7 | 18.93 |
„ 2.5 | 3 | 72.56 | 3.5 | 50.73 | 4 | 39.74 | 4.5 | 32.85 | 5 | 28.07 | 5.5 | 24.54 | 6 | 21.83 | 6.5 | 19.66 |
2 | 2.5 | 81.27 | 3 | 55.48 | 3.5 | 42.78 | 4 | 35.00 | 4.5 | 29.68 | 5 | 25.80 | 5.5 | 22.82 | 6 | 20.47 |
„ 1.5 | 2 | 93.1 | 2.5 | 61.54 | 3 | 46.55 | 3.5 | 37.28 | 4 | 31.56 | 4.5 | 27.23 | 5 | 23.96 | 5.5 | 21.39 |
„ 1 | 1.5 | 110.4 | 2 | 69.66 | 2.5 | 51.34 | 3 | 40.75 | 3.5 | 33.82 | 4 | 28.91 | 4.5 | 25.26 | 5 | 22.43 |
„ 0.5 | 1 | 138.98 | 1.5 | 81.30 | 2 | 57.67 | 2.5 | 44.75 | 3 | 36.55 | 3.5 | 30.91 | 4 | 26.77 | 4.5 | 23.61 |
Stationary 0 | 0.5 | 200 | 1 | 100 | 1.5 | 66.66 | 2 | 50 | 2.5 | 40 | 3 | 33.33 | 3.5 | 28.57 | 4 | 25 |
Diminishing — 0.45 | 0.05 | 510.54 | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
„ -0.5 | 0 | 8 | 0.5 | 138.28 | 1 | 80.89 | 1.5 | 57.39 | 2 | 44.52 | 2.5 | 36.37 | 3 | 30.75 | 3.5 | 26.64 |
„ -0.95 | ... | ... | 0.05 | 313.84 | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
„ -1 | ... | ... | 0 | 8 | 0.5 | 109.31 | 1 | 68.97 | 1.5 | 50.93 | 2 | 40.34 | 2.5 | 33.48 | 3 | 28.62 |
„ – 1.45 | ... | ... | ... | ... | 0.05 | 232.86 | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
„ -1.5 | ... | ... | ... | ... | 0 | 8 | 0.5 | 91.72 | 1 | 60.63 | 1.5 | 45.86 | 2 | 37.03 | 2.5 | 31.10 |
„ -1.95 | ... | b=birth-rate of one unit for one year | 0.05 | 187.32 | ... | ... | ... | ... | ... | ... | ... | ... | ||||
„ -2 | ... | d=death-rate „ „ | 0 | 8 | 0.5 | 79.66 | 1 | 54.38 | 1.5 | 41.94 | 2 | 34.31 | ||||
-2.45 | ... | r=increase „ „ =b—a | ... | ... | 0.05 | 157.71 | ... | ... | 1.5 | ... | ... | ... | ||||
„ -2.5 | ... | x=number of years, or mean duration of life | ... | ... | 0 | 8 | 0.5 | 70.77 | 1 | 49.47 | 1.5 | 38.74 | ||||
„ -2.95 | ... | (1+r)x=b/d | log. b/d x= log.(1+r) | ... | ... | ... | ... | 0.05 | 136.73 | ... | ... | ... | ... | |||
„ -3 | ... | ... | ... | ... | ... | 0 | 8 | 0.5 | 63.89 | 1 | 45.52 | |||||
„ —3.45 | ... | ... | ... | ... | ... | ... | ... | 0.05 | 121.01 | ... | ... | |||||
„ —3.5 | ... | ... | ... | ... | ... | ... | ... | 0 | 8 | 0.5 | 58.37 | |||||
„ —3.95 | ... | ... | ... | ... | ... | ... | ... | ... | ... | 0.05 | 108.73 | |||||
„ -4 | ... | – | ... | ... | ... | ... | ... | ... | ... | ... | 0 | 8 |