On Rates of Mortality and their Causes. By W. LAZARUS, of Hamburg, Actuary of the General Insurance Company of Trieste. Translated by T. B. SPRAGUE, M.A., Manager of the Scottish Equitable Life Assurance Society.

(Continued from page 61.)

WE are so accustomed, even when we do not aim at scientific

exactness, to regard every phenomenon as produced by causes,- -as the resultant of forces,-that we cannot help looking on what we call "life" as the effect of certain definite forces, and on death as the consequence of the extinction of those forces. But when we thus contrast life and death, we must always bear in mind not only that what we call "life" is a condition which presents itself under circumstances of unexhaustable variety, but that in all probability quite as many differences in its manifestation entirely elude our observation. Given the effect, we reason as to the cause; when the effects are different, we infer that either the causes are different, or the conditions on which the effect depends. But if the differences are so numerous that we can scarcely find two cases exactly alike, we can draw no conclusion either as to the causes or as to the conditions. Since in no single case can we recognize the various conditions under which the cause of life works, we cannot hope to decide how the effect is connected with the conditions and how with the causes. Death too is a phenomenon as to which we have not the least idea why it happens; whether because the vital force in the individual has sunk below a certain degree which is necessary for the maintenance of life, or whether as a result of wholly different forces. On this point we scarcely know more than that the possibility of organic life depends upon certain conditions, that it can exist so long as these conditions remain within limits more or less wide, and that a transgression of the limits causes death. We do not, however, know exactly what these conditions are, and still less do we know the limits within which human life can exist; and if we reflect how complicated are the circumstances to be taken into account, we can scarcely hope to see these relations settled for some time to come. It is further to be observed that life, being regarded as the effect of a force, and death as its extinction, there must be a gradual transition from the one to the other. But the contrast between them is so complete that we are quite unable to measure the diminution of life, for the purpose of inferring the magnitude of the force that supports it. Altho' it is in complete harmony with our ordinary conceptions to

speak of the gradual diminution of the force which sustains life, and altho’in many cases we observe a slow transition from life to death, we must yet wholly abandon the idea of measuring the intensity of life, because it is a phenomenon of which the manifestations are so various.

It is only by means of observing large numbers that we can obtain another starting point. Combining into a group a sufficiently large number of new-born children, and considering this group as a unit, we can disregard all minor matters and take the number surviving at any time as a measure of the vital force then existing in the group. The deaths that occur from time to time will then show us how the vital force contained in the group gradually decreases; and we thus find that the gradual dying out of the group, or the extinction of its aggregate life, proceeds with perfect regularity. If, on the contrary, we resolve the group again into its single elements, we can no longer find in them the regularity that we observed in the group.

When the observation of large numbers thus exhibits clearly a regularity in certain respects which is not perceptible among smaller groups, we shall be justified in fixing our attention exclusively upon the cause of this regularity. Though, possibly it is one part of a force which produces at one and the same time altogether different effects, according to the conditions which it meets with, yet there is nothing to prevent our considering a cause as consisting of different parts, of which one or several operating alone produce the precise effect we have observed. If we consider the decrease of the vital force as a cause which occasions in individuals, sometimes sufferings of the most varied kinds, bodily or mental, sometimes sickness, sometimes death, so that these different effects, depending upon conditions unknown to us, appear to be wholly irregular, capricious, and incapable of being foreseen, yet we know that in observing large bodies of persons, each of these effects appears with perfect regularity; and we are even entitled to attribute each of these effects to a corresponding part of the general cause,- —a part which we can imagine separated from the whole; and with reference to the effect in question we may fix our attention exclusively on this part of the cause.

This analysis of causes is, I believe, the chief means by which the observation of large numbers can be applied to the discovery of new truths. The nature of the causes and the forces is absolutely hidden from us; but in all cases in which an effect is recognized, we infer the existence of a cause producing it. The simpler the

effect, and the more distinct from other phenomenons, the sooner and the more thoroughly do we succeed in analyzing the causes; but in cases where a thousand different effects of the same cause constantly cross each other, where not only are a large proportion of the effects such as we cannot measure, but a perhaps still larger proportion altogether elude our powers of observation, it becomes impossible to draw any conclusion as to the cause. In such cases we call to our assistance the method of observing large numbers, registering separately each of the different effects so far as they are visible; and whenever this method can be applied, instead of a confused mass of tangled threads, the general design becomes apparent, in which the separate lines run with great regularity. The observation of large numbers by thus resolving the irregular phenomenons into regular ones, at the same time decomposes the cause into parts corresponding to the various partial patterns which make up the whole design. Altho' probably all these different patterns, and many others which have not yet come within our range of vision, should be considered as the total effect of one and the same cause, yet we appropriate to each pattern its own special portion of the total cause, and treat this as if it had an independent existence. Since we know nothing about the nature and essence of the causes in general, it is quite immaterial in what way we picture to ourselves this decomposition of the cause. It is also immaterial whether we consider the cause itself as split up, or whether we imagine the coexisting conditions as grouped, for the effect only takes place if the cause meets with the necessary conditions, and consequently the latter really form part of the cause. Even in simpler subjects, we constantly have causes analyzed and separated; for instance, we consider the weight and impenetrability of matter as two separate causes of different phenomenons, altho' we know of no single instance in which the effects of the one appear without those of the other; so, again, we know that in every chemical combination heat is set free, and yet we consider chemical affinity apart from heat. It should certainly not be difficult to prove that in general we never see an effect towards the production of which more causes than one did not contribute; but this does not in the least prevent us from fixing attention exclusively upon a single cause and investigating its action independently of all others. We proceed in just the same way with regard to the phenomenons the regularity of which is made known to us by the observation of large numbers. We consider each as the effect of a definite cause, or what is the same

thing, as the effect of a certain part of a cause that operates in different directions; and we disregard entirely the effect of its other parts when we refer each regular series of phenomenons to a separate cause.

The processes of meteorology may be cited as an example. In these, too, we have to do with phenomenons which are so manysided and complex as not to admit of a conclusion as to the causes that produce them. Meteorology can scarcely be considered a statistical science; but the statistical method is applicable to it. This method distributes the phenomenons into distinct groups; and as soon as we see in these groups a steady regular progression, we infer that there is a cause producing this progression, and consider it as a partial cause, under certain conditions, of meteorological processes in general, and then perhaps proceed to examine what these conditions are. Thus by observing large numbers we succeed in recognizing particular parts of the causes, their effect being exhibited distinct from the effect of the other parts. But if, from the total pattern given by the statistical method, we would draw conclusions as to a smaller group or an individual, it must be borne in mind that we shall not in this case find the same pattern on a reduced scale. The total cause, which produced in the whole group completely regular phenomenons, appears to operate quite irregularly in the smaller groups and in the individual- —a fact fully explained by the complexity of their method of operation.* This might perhaps be represented by saying that the same cause operating upon a large number of individuals produces an extensive series of different regular patterns by arranging those individuals in certain groups; but that this mode of operation cannot be recognized if, instead of observing the effect on the large number of persons, we observe only the effect on a few of them. Supposing, on the other hand, that the arrangement in each single group is characterized by a regularity of its own, the observation of one group would suffice to enable us to draw conclusions as to a partial effect of the cause, or what is the same thing, as to a part of the cause itself, disregarding altogether its other parts. Whenever then we would use the results obtained from the observation of large numbers, to draw conclusions as to smaller groups and individuals, we must bear in mind that the elements of the large group are not all precisely similar, that there are, on the contrary, among them elements of deviation in different directions; but as these

* We remind the reader of a very closely allied method of investigation applied in the calculus of probabilities.