Age. Comparative View of Number of Survivors at Different Ages according to various Life Tables. (Ogle.) 10 New English. Old Healthy Males Healthy Districts 98 96 93 89 84 79 74 67 60 51 42 31 20 98 94 90 86 82 77 72 66 59 52 43 32 21 98 96 93 90 86 82 78 73 67 59 49 38 26 98 96 92 89 85 81 77 73 68 62 53 43 30 Upper Class Experience 98 95 91 87 83 79 75 70 65 59 51 43 ? Clerical 15 New English. Old Healthy Males Healthy Districts 98 94 90 86 81 75 68 61 52 43 32 21 Upper Class Experience 97 93 88 84 80 76 71 66 60 52 43 ? 97 93 88 83 77 70 62 54 44 33 21 Upper Class Experience 96 91 87 83 78 73 68 62 54 45 96 91 86 79 73 65 56 45 34 22 95 90 85 79 73 66 57 47 36 24 97 93 88 84 78 71 63 53 41 28 Upper Class Experience 95 91 86 82 76 71 65 56 47 ? 95 89 83 76 67 58 47 35 23 95 89 83 77 69 60 49 38 25 96 92 87 81 74 66 55 42 29 96 92 87 82 77 70 60 48 34 Upper Class Experience 95 91 86 80 75 70 59 49 ? 94 88 81 73 63 52 40 26 95 90 84 77 68 57 44 30 Upper Class Experience 95 90 84 79 71 62 51 ? Clerical 96 92 87 81 72 62 49 35 From this valuable table, arranged by Dr. W. Ogle (Journal of the Statistical Society, vol. vii. pt. iv. page 640), a comparison can readily be made between several Life Tables based on the mortality of males, and the influence of social or other conditions on vitality can be approximately estimated. The ages to which the percentages apply are given in the first vertical column to the left of the page, and the percentage of males surviving 5, 10, 15, etc., years, according to the several Life Tables are given in the horizontal columns. The comparison between the old and new English Tables shows that in 1838-54 the chances of life were less favourable at the younger ages, and more favourable at the older ages, than in 1871-80. For instance, of 100 children just ten years old, 86 would survive 20 years by the old table, and 82 by the new Table; but after an interval of 50 years (i.e., at 60 years of age) 52 would survive by the old, and 51 by the new table. The Healthy Males Table being founded on insured and therefore selected lives, shows a considerably larger percentage of survivals throughout than does the English Life Table. A comparison of the upper-class experience table with the old English Life Table shows the effect of more favourable social circumstances; and were the figures for ages under 10 given, the comparison would be much more in favour of the upperclass table. For short periods the chances of survival are not widely different; but when the chances of survival for longer periods are considered, the differences are very great. Thus, of 100 children just 10 years old, 32 live 60 years longer by the old English Life Table, and 43 by the upper-class table; and of 100 men 55 years old, 87 are alive after 5 years interval by the English Table, and 91 by the upper-class table. In comparing the clerical experience table with the upperclass table, the advantage is largely on the side of the clergy in all the periods of life, except for the later ages or for long survivals. It is not easy to see any satisfactory explanation of this, and Dr. Ogle suspects that one or other of these tables has been based on too small a number of observations. CHAPTER XV. THE DURATION OF LIFE. Connection between Mean Age at Death, Expectation of Life, and Number out of which One Dies Annually.-Mean Age at Death.-Effect of BirthRate on Mean Age at Death.—Mean Age at Death from Certain Diseases. -Mean Age of Living.-Mean Duration of Life.-Complete and Curtate Expectation of Life.-Willich's and Farr's Formulæ.-Probable Duration of Life.-Specific Intensity.-Probability of Living a given Number of Years. Probability of Dying of any one Disease. THE THE duration of life is the problem with which Vital Statistics are largely occupied. As Babbage has put it, "Nothing is more uncertain than the duration of life when the maxim is applied to the individual; but there are few things less subject to fluctuation than the duration of life in a multitude of individuals." It is on this principle that annuities and life assurances can be made the subject of definite and exact calculations, the final results being found to vary within very narrow limits. Several tests are employed to measure the duration of human life, and we are at present concerned to determine their precise value, and the relationship existing between them. Those most commonly employed are: (1) The mean age at death; (2) The probable duration of life; (3) The mean duration of life; (4) The expectation of life, or mean after-lifetime; Before discussing the value of these different tests of vitality, the student should understand the close relationship (amounting to numerical identity) which exists between the mean age at death, the expectation of life, and the number out of which one dies annually, in a Life-Table or normal population. In a Life Table, of which an elementary specimen is shown below, it is evident that the number against any age in the second column is equal to the sum of those in the third column against that and all the greater ages; from which we infer that the number who complete any year of age is equal to the sum of those dying at all the greater ages. Thus in the table, the number who annually complete their ninety-sixth year (=14) is equal to the sum of the annual deaths at all the greater ages. On the assumption that the deaths in any year are distributed at equal intervals in the year, it follows that the number living in any year of their age, such as would be ascertained in a census enumeration, is an arithmetical mean between the number entering upon and the number completing that year. |