gument could never perfectly settle it, however plausible and ingenious the grounds of the prejudgment and argument might be. It is one of those allegations, the accuracy or inaccuracy of which is a matter that can be fully and finally determined by one method only,— namely, by an appeal to the evidence of facts, and to the evidence of facts alone. For the purpose of assisting in the decision of this question, I have, through the great kindness of my professional brethren, collected the results of above three hundred amputations of the thigh, leg, arm, and fore-arm, performed within the last six months upon patients in an etherized state, in the civil hospitals of England, Scotland, Ireland, and France. The statistical analysis of these three hundred amputations with ether, and the comparison of their results with the results of various similar collections of the same amputations without ether, in the same and in other similar hospitals, will, I believe, enable us to arrive at some more definite ideas and deductions than we are yet in possession of, in regard to the debated question of the danger or safety of etherization in the operations of surgery. But let us first inquire if this statistical method is the proper method of investigating such a subject.

CHAPTER V.

VALUE AND NECESSITY OF THE NUMERICAL METHOD OF INVESTIGATION AS APPLIED To surgery.'

"La possibilité de l'application de la statistique à la médecine, est une verité tout aussi bien demontrée que la realité de la circulation."-Dezeimeris, Dictionnaire de Médecine, vol. xxviii. p. 550.

THE vast practical importance of the doctrine of statistics, and its power of elucidating, simplifying, and deciding many and various inquiries in surgical and medical science, is now becoming daily more and more acknowledged by the members of the profession. The doctrine itself has been long, not only acknowledged, but acted upon by governments and by the public at large. The political laws and expensive machinery pertaining to the registration of the deaths and diseases of the inhabitants of England, and of other kingdoms of Europe, are founded upon the soundness of the doctrine. In our numerous life assurances and annuity companies, millions of money are unhesitatingly staked upon the truth of it. And the principle upon which the usefulness and stability of the whole doctrine of medical statistics rests, is a very simple one. It amounts to

1 From Edinburgh Monthly Journal of Medical Science, Nov. 1847, p. 13.

this: Among facts, data, or unities of a variable chance-such as the probabilities of death within a given time, or the probabilities of attacks of particular diseases within a given time, or the probabilities of averting death in particular diseases by particular methods of treatment, or operation-there is ever a mighty uncertainty as to the results, if we consider only single cases, or a small and limited number of instances; but our results approach more and more to certainty, in proportion as we deduce these results from a greater and more extended number of instances-from a larger and multiplied series of facts. There is always great uncertainty and instability in regard to the results of single or isolated cases; but a proper aggregation and conjunction of cases affords results which are comparatively certain and stable.

In the present investigation into the effects of etherization upon the mortality attendant on surgical operations, I have followed the statistical method of inquiry. But as the doctrine itself of statistics, as applied to such questions, is still, I fear, very imperfectly understood by the profession in this country, I shall here take the liberty of premising a few observations upon this mode of inquiry.

I have already stated, that the great and leading principle upon which all statistical inquiry is grounded, consists in the fact, that in unities or entities of a doubtful chance, while the result, or event, in individual instances, is ever variable and uncertain, the result, or event, when calculated from, or upon masses of instances, becomes comparatively certain and invariable. I shall show the truth of this abstract remark, in the form of illustrations, of a few of the fundamental principles or propositions upon which the doctrine of medical statistics is founded, and this more especially with a view to the bearings and important advantages of the statistical or numerical method of inquiry as applied to questions in surgery.

FIRST PROPOSITION.

The absolute number of deaths from all causes, in a given time, in a given population, is always nearly the same.

The probability of life or death to individuals within the limits of a given period, is proverbially uncertain. Nothing is more uncertain, for instance, than the number of individuals that will die in the currency of a single year in any particular family, street, or village in England and Wales. But nothing could be more certain than, cæteris paribus, the number that will die during the currency of a single year in the whole of England and Wales. Estimating, for instance, as we do in all modes of reasoning and philosophizing, from the experience of the past what will be the experience of the future under similar circumstances, we may state

beforehand as certain, that in 1845 (the results of which have not yet been published) the total number of deaths in England and Wales amounted to about 350,000. For the returns of the Registrar-General for England and Wales have now been collected and published for seven years-viz., from 1838 to 1844 inclusive, and the total numbers that died during each of these years were fixed and determinate, to the extent shown in the following table:

No. 1.-Table of Absolute number of Deaths in England and Wales and of the percentage of Deaths among the whole population during the seven successive years from 1838 to 1844 inclusive.

In reference to the preceding table, we must bear in recollection one point, that in this, as in other statistical inquiries, there is always a range of oscillation, and limits of possible error; but, as Gavarret has well demonstrated, the extent of these oscillations and limits of possible error are themselves easily ascertainable, and capable of being reduced to mathematical calculation and correction.

SECOND PROPOSITION.

The absolute number of deaths from individual diseases and specific causes in a given time, in a given population, is always nearly the same.

For if it be true, as shown under the first proposition, that the exact number dying annually in England is nearly the same, it is equally true and demonstrable that the particular causes or forms of disease producing these deaths recur in successive years in the same number and proportion. What is true regarding the whole, is true in regard to its parts. For the purpose of illustrating this secondary fact, I shall take from the Registrar-General's reports nine returns, three referring to medical, three to surgical, and three to obstetric affections and complications; and I shall add one pertaining to the department of medical jurisprudence. Each of them shows the comparative certainty of large numbers. For while, for example, no man could predict who or what number of a small community would die annually of croup, or tetanus, or ovarian dropsy, yet the absolute number dying each year of these and other affections throughout England, when calculated on a large scale,

comes annually, in all except epidemic and zymotic diseases, to be nearly the same, as the following table sufficiently demonstrates. In fact, their numbers are, if possible, more determinate than the numbers of the total deaths; because, while the absolute mortality of a kingdom is liable to be varied by variations of a temporary and transient nature in the existing epidemic and endemic influences, &c., those individual diseases and causes of death, the etiology of which is more fixed, are more stable in their results:

No. II.—Table of Absolute number of Deaths annually in England and Wales from twelve different Diseases or Causes of Death.

The regularity with which the same disease thus destroys in successive years, nearly the same number of individuals, may appear remarkable to those who have not given attention to the study of medical statistics, and who have, consequently, not marked the fixed and determinate nature of the results which this means of investigation always elicits, when it is enabled to work upon a sufficiently large basis of facts, or a sufficiently large series of data. But this constancy appears, if possible, still more singular, when we return to such a subject as that included under the last column in the table viz., "violent deaths." Under this head are included deaths by mechanical injuries, by chemical injuries, by asphyxia, &c., and, if the returns were more specific, it would no doubt be found that the number of violent deaths from each separate division of causes was annually nearly the same. Even causes originating in passions of the human mind, and leading to violent death by murder are, cœteris paribus, repeated in nearly the same number in each successive year. The moral man is subject to laws as fixed as the physical man. Some years ago, Quetelet showed, from the comparison of the annual number of deaths in Paris, and the annual number of crimes committed throughout France, that the statistics of human crime are as fixed as the statistics of human mortality; that each age paid

as uniform and constant a tribute to the jail as it paid to the tomb; that the numbers of any specific crime in successive years was, like the numbers of deaths from any specific disease in successive years, always nearly the same; ay, that the very instruments by which the same crime (as murder) was perpetrated in different years, were always in nearly the same proportion.1

THIRD PROPOSITION.

The absolute number of those that recover should, cæteris paribus, be as fixed as the number of those that die, from individual diseases in a given population.

The preceding table (No. II.) shows how many died of the several affections included under it, during a succession of years. If our statistics were more specific and detailed, we ought to be able to tell also how many recovered each year from attacks of each of these affections, as well as how many died from them; and if we could thus count the number of recoveries as well as the number of deaths by striking the proportion between them, we should obtain the average mortality of each disease. The deaths, for instance, from croup, amount on an average to 4325 each year. But if at the same time we knew the total average number of cases of croup that occurred every year (say, for the sake of illustration, that they amounted to 13,000 in all), then the mortality of the disease would amount to nearly 1 in 3; or out of every three patients attacked with croup, two would recover and one die.

1 "If all human actions could be registered," says Quetelet, "it might be supposed that their numbers would vary from year to year as widely as human caprice. But this is not what we in reality observe, at least for that class of actions of which we have succeeded in obtaining a registry. I shall quote but a single example; but it merits the attention of all philosophic minds. In everything which relates to crimes, the same numbers are reproduced; so constantly, that it becomes impossible to misapprehend it—even in respect to those crimes which seem perfectly beyond human foresight, such as murders committed in general at the close of quarrels, arising without a motive, and under other circumstances to all ap pearance fortuitous or accidental. Nevertheless experience proves that murders are com mitted annually not only pretty nearly to the same extent, but even that the instruments em ployed are in the same proportions."-Treatise on Man, p. 6. The following table, abridged from Quetelet, may enforce still more the truth of his observations.

Table of the Annual Total Number of Murders, and Instruments of Murder, in France, collected from the Reports of Criminal Justice, from 1826 to 1831.

The difference in 1830 and 1831 from the preceding four years was no doubt owing, in a great degree, to the Revolution of 1830 and its immediate effects.