VVESTERGAARD'S " FUNDAMENTAL OUTLINES OF STATISTICAL THEORY." * OF all

the sciences, that of Statistics appears probably to many the dullest and most repulsive. And yet it is not too much to say that it has its imaginative, one might almost say its poetic side. What human act would appear to spring from more various causes, to be influenced by more various circum- stances, than that of suicide P Is not the man at first sight a romancer who would tell us that, viewed on a sufficiently large scale, such an act is subject to definite laws, and is capable of almost exact calculation, and that for each sex?

Yet nothing is more certain. In the twenty-six years 1861- 1886, the total actual number of female suicides in Denmark was 2,803 ; the calculated number was 2,809, a difference of six only. The very modes of death are calculable. For the same period, the actual number of suicides by hanging was 8,108 for men, 1,569 for women ; the calculated numbers were 8,107 and 1,568, a difference of one only on each. The very numbers in a given month may be calculated with scarcely less exactness. Thus, during the same period for the month of October, the actual numbers were, for men 1,952, for women 573, whilst the calculated ones were 1,954 and 574. Is it wonderful that the glimpses thus obtained of an order in seeming chaos, of laws ruling that which at first sight shows itself as most wilful or most fortuitous, should exercise over some minds a real fascination P Professor Westergaard's new work—the simultaneous ap- pearance of which both in a German and a Danish form shows sufficiently the importance attached to it on the Continent— puts forward very clearly in its opening words the claims of statistical science upon human attention :-

"If one considers human society in its life and action, one may at the first glance perceive in the most various fields a surprising regularity. Every year, for instance, in any country or class of the population, about the same number of marriages take place, and the figures for births and deaths, for suicide and crime, recur fairly regularly from year to year at the same level. Whether it be the results of games of chance, or those of postal and railway traffic, of navigation and trade, upon all is impressed a certain stamp of regularity. Thus, for instance, it will be observed that in this century the number of births in Denmark in its relation to population only once—in the year 1832—fell below 3 per cent., but otherwise oscillated between 3 and 31, that in the same country, during the last decade, from 10 to 11 per cent. of the births were illegitimate; that the frequency of suicide fluctuated within narrow limits, about the figure of 27 per cent. of the population. An example of a different sort is offered by a series of experiments communicated by Quetelet,—viz., that a ball was drawn 4,096 times out of an urn containing an equal number of white and black balls, with the result that 2,066 drawings gave a white, and 2,030 a black ball, so that out of a thousand balls

there were 504 white and 496 black Now this stability in matters of number has a high practical import. It alone makes it possible to fix a picture of human society ; it enables us to draw conclusions for the future, and thereby to exercise in the most

various relations a beneficial influence on social life On the ground of this regularity, one can establish a science of numbers—statistics. Its task is not only to determine before- hand the most accurate numbers and measures possible, to supply carefully collected and trustworthy materials, and therefrom to sketch a true picture of the present state of society, but also to provide the conditions under which this regularity shall show itself, so as to give a rational foundation to anticipatory calcula- tions. This means nothing else than the teaching of causes, and the understanding of numerical facts as results of a chain of influencing forces."

Having thus laid down his principles, Professor Westergaard proceeds to treat of the conditions of regularity, of conformity to law in games of chance, on the application to social statistics of the experience so gained ; the leading principles

• Harald Westergaard Staristikens Theori i Grundrigs. Ejobenhavn : P. S. Phil( 1891—Die Grandees der Theorie der Statistik. Von Harald Wester - Protessor an der Univeraitiit au 'Copenhagen. Jena : Gustav Fischer. 1890 .

of the calculation of probabilities, the treatment • of the materials so acquired ; interpolation and adjustment of popu- lation, the movement of population, the bodily and mental qualities of population, economic statistics, insurance. Lastly, in the historical part, he treats of the materials of statistics, of statistics till the beginning of the nineteenth century, and in the nineteenth century. Everywhere we find evi- dences of wide reading, in reference to German, English, French, Italian authors, as well as to those of his own and other Scandinavian countries ; and of independence of thought in his treatment of the authors referred to. There is even a spice of grave humour in his critique on the dashing and dazzling Belgian theorist, Quetelet, the type of whose

mind is, indeed, the very opposite to that of the Danish Pro- fessor. Speaking, for instance, of Quetelet's celebrated homme moyen, of whom he would make the centre of gravity of society, he says :— " So long as this imaginary being is only considered as a unit of account, this may well consist with the principles of statistical science, which continually occupies itself with averages; but Quetelet is always trying to provide the average man with flesh

and blood According to Quetelet, the average man should possess ideal beauty ; he would be the type upon which, so to speak, Nature fashions all men with varying success ; and the study of the average man would thereby have great importance in art The untenableness of this theory strikes the eye at once, even while leaving altogether out of account the impossi- bility of constructing a man out of a number of average qualities ; the average colour of the eyes would not correspond to the demands of beauty, and an average profile would certainly be far

from ideal beauty As the physical average man repre- sented for Quetelet the ideal of beauty, so the moral average man was the possessor of ideal spiritual strength, and represented the ideal of goodness, notwithstanding his coverage propensity to crime."

To the student, indeed, Professor Westergaard's work is invaluable through its insistence on the importance of facts. " The nicest calculation," he says in one place, " cannot take the place of direct observation ; one must therefore always put it to the proof, whether the results of calculation agree with experience." And again: "The best hypothesis cannot take the place of one exact observation ; it is better to observe than to guess, with however much of foresight and method." It is equally invaluable through its careful limitation of the province of statistics. In his interesting chapter on " the Bodily and Mental Qualities of Populations," when he comes to the head of so-called " Moral Statistics," he is careful to point out that one can only deal with certain outward tokens of the

soul's life. One may reckon the number of committed murders, but not of attempts to murder ; one may find the number of acts of an ecclesiastical character, but there can be no statistics of the actual religious sentiment ; nor can the number of marriages tell us anything of the great number of

cases in which people would have been glad to marry, but have remained single for one cause or another. Yet this

strict limitation of the field of statistical science only makes the writer's observations more valuable, even in respect of subjects in which he has received no special training, —e.g., criminal statistics (since Professor Westergaard is not a lawyer). The work may, indeed, be said to be specially adapted to an English public rather than to the German one

to which, in its translated form, it addresses itself. Nothing is evolved from the " inner consciousness " of the writer ; he is severely critical in the handling of every problem, studiously cautious in every deduction. A little more carefulness as to style might easily raise many passages to a grave eloquence.

The book would perhaps have gained in interest for the general reader if, after outlining his subject, the author had made the history of statistics the first part of his work instead of the last, and, indeed, if a more historical treatment had been adopted throughout. A remark may also be made on the use by Professor Westergaard of the term "interpola- tion," new to statistical theory ; by this he designates all hypothetical calculations deduced from actual figures, as when, from a census of the population and a census of cattle taken in two different months, one seeks to calculate the number of cattle per inhabitant. The term is certainly a con- venient one, though it hardly perhaps commends itself at first sight, and there remains to be seen whether its con- venience will bring it into general use.

It may be mentioned that Professor Westergaard is already the author of a valuable work (also•published in German) on

mortality and disease, dedicated to the present President of the Institute of Actuaries (Die Lehre von der Mortalitdt and

.Morbilitdt, Jena, 1882), and that his Fundamental Outlines of Statistical The4ry have already been followed by a. work drawn up by him in tonjunction with the Director of the Statistical Office of Copenhagen City, upon the statistics of marriage, on the basis of the social distribution of the population, from censuses and church registers in Denmark,* which, although less adapted to the general reader or the inquirer, contains much carefully drawn up and valuable matter for the professional statist. We find here from Danish records a confirmation of the observation often made of the tendency of young widowers to marry again. Thus, the per-tentage of Danish widowers to bachelors marrying in the years 1878-82 was 6S per cent., as against 8; and whilst out of 100 bachelors of 25 who reached 45,12 remained unmarried, out of 100 widowers of the same age, there was only 1. A similar tendency shows itself amongst widows.