New Mortality Experience. HMF, &c.-(continued).

ON HERR LAZARUS'S PAPER ON THE THEORY OF
PROBABILITIES.

To the Editor of the Journal of the Institute of Actuaries.

SIR,-In the July number of the Journal you inserted a letter from me, having for its object the elucidation of a passage in Herr Lazarus's paper "On some problems in the Theory of Probabilities." I have since received a very courteous communication from Herr Lazarus in reference to the subject of my letter; and I beg to send you the substance of that communication out of fairness to Herr Lazarus, at the same time feeling confident that it will greatly interest some of your readers.

He says, in explanation of the passage upon which my remarks were based, "The simplest way to find the sum 20+1+22 would be to extend one of the equations (28) or (29), so as to include 20. I think it is self"evident from (28) that

66

With regard to the signs of the first two terms in this expression, Herr Lazarus says, "On page 246, at the bottom, we found the inequalities

There is thus, then, no necessity for the double sign which I prefixed to these terms. At the same time I think it would have been as well, had this step in the demonstration been inserted in Herr Lazarus's paper.

Herr Lazarus kindly points out a misprint in my letter. In the expression for +1 +22, on page 454, the factor has been omitted

1

Υπ

from the first two terms.

I am,
Sir,

Dec. 1, 1870,

18, Lincoln's Inn Fields.

Your obedient servant,

WILLIAM SUTTON.

JOURNAL

OF THE

INSTITUTE OF ACTUARIES

AND

ASSURANCE MAGAZINE.

On the effect of Migrations in disturbing Local Rates of Mortality, as exemplified in the Statistics of London and the surrounding country, for the Years 1851-1860. By THOMAS A. WELTON, F.S.S.

[Read before the Institute, 19th December, 1870.]

Introduction.

I PROPOSE in this paper to deal with a question which has an important bearing upon those calculations as to deathrates, which are now so widely circulated and so generally felt to possess interest.

It has occurred to the Registrar-General, and, as I believe, to other inquirers, to remark that the mortality happening in London is diminished, "because domestic servants, shopwomen and milliners, "who have come from the country, retire when health fails them "to their native air."

It is obvious that the resort of sick persons to country districts would produce an effect on the mortality in such districts of the opposite nature. And I suppose that few would be surprised if it were found that places on the south coast, to which persons suffering from consumption and other ailments are apt to remove, exhibited heavy deathrates. But I do not think that the aggrava

VOL. XVI.

M

tion of mortality at ages 15-35, which happens in the most obscure districts and amongst the humblest families, has ever been thoroughly appreciated, or more distinctly pointed to than it is in the paragraph just quoted.

Researches into the comparative mortality occurring in different parts of Lancashire and Cheshire led me to perceive

(1) that a striking depression in the mortality of Liverpool (with its environs*) at ages 10-35 coincided with the circumstance that enormous numbers of immigrants, both from Ireland and from parts of England and Wales, served to sustain the rapid increase of population, for which that unhealthy town is remarkable; and

(2) that in the rural districts of North Lancashire, which lose a portion of the natural increase of their inhabitants by emigration, there was a slight rise in the relative rates of mortality at the same ages:—

Males. Females. Males. Females. Males. Females. Males. Females. Males. Females.

It will be seen that at ages 0-10 and 45-65 Liverpool is very unhealthy for both males and females. At the same ages North Lancashire is not unhealthy; indeed, at ages 0–5, the mortality there, of both boys and girls, is little more than one-half that observed in Liverpool.

But at ages 15-25, the female deathrates in North Lancashire are much higher than in Liverpool. And at ages 15-65, the female deathrates in Liverpool are depressed as compared with the male deathrates; the contrary being the case in North Lancashire. The Districts of Liverpool, West Derby, Birkenhead, Wirral, Prescot, and Orms

kirk.

The general aspect of the figures is consistent with an idea, that the normal rates of mortality in Liverpool are from 30 to 40 per cent. higher than the English rates; but that they are depressed, through the operation of some special causes, between ages 10 and 35, and that such causes have a greater influence over the female than the male sex.

There are so many diverse attractions influencing the migrations of natives of Lancashire and Cheshire, that to identify any large district as the principal "recruiting ground" of the population of Liverpool, is out of the question. But the problem as to the effect of migrations on rates of mortality having once been seen to possess great importance, I was led to consider the question, where a better example could be found. And I concluded that the most important instance, and the one which promised to repay the most careful investigation, was that of the Metropolis and the surrounding counties.

The figures for the Metropolitan Division correspond in a remarkable manner with those just given for Liverpool and its neighbourhood::

With hardly an exception, these ratios rise and fall together, London being throughout less insalubrious than Liverpool, and both places being apparently most healthful for persons at the age 15-20.

On referring to the observed mortality in the Eastern Counties, whence so many of the working class in London are derived, and where comparatively few persons choose to reside for the benefit of their health, we have the following ratios: