As an example of an event brought about by a multitude of causes may be mentioned the event of death, governed, as to the age at which it occurs, by original strength or pecu liarity of constitution, good or bad nursing and management in infancy, sex, occupation and habits of life, climate and place of abode, skilful or unskilful treatment in sickness ; in a word, by the varied influences which make one man to differ physically from another. This is an illustration taken from the science of hygiene. The alternative of death or re covery from a disease induced by a cause or causes of variable intensity in persons of opposite sex and of different ages, with con stitutions modified by the several agencies just specified, and submitted to different modes of treatment, is an example from the practice of medicine. Physiology furnishes illustrations of the same kind in those func tions of the body (such as the cutting of the teeth, and the first appearance and cessation of the catamenia) which are dependent for the period of their occurrence on peculiarity, of constitution determined by the combined action of the influences already adverted to.
Between these two orders of facts — phe nomena of varying intensity, and events brought about by a multitude of causes there is no other difference but that which is apparent on the face of each, namely, that each individual fact, in the one case, is repre sented by a variable number, while in the other it is a simple unit. If, for example, we count the pulse of several men at the same age, we shall find that each separate observa tion gives a different number ; but, the event of death or recovery in cases of typhus fever will be recorded as a simple unit. In all other respects the two classes of facts closely re semble each other; for the number of beats peculiar to the pulse of each individual, is as much the result of the concurrent action of several causes, as the event of death or reco very from fever. The original and acquired constitution, towards the formation of which so many causes must have conspired, deter mines the number of the pulse in the one case, and influences the event of the disease in the other. The two classes of facts are also equally fitted to supply the elements for the determination of average and extreme values; for it is obvious that the mean and extreme numbers of the pulse, in males and females respectively, furnish as trustworthy standards of comparison and data for reason ing, as the average number of men following different occupations who die before any spe cified period of life, and the greatest age which they respectively attain.
From what has been just stated, it will be seen that all the facts which form the mate rials for our averages, are phenomena or events brought about by the concurrent action of a multitude of causes. The facts or events with which the physiologist and physician are conversant, are remarkable for the mul tiplicity of the causes which conspire to pro duce them. The subject of study is the hu man frame, with its differences of sex, age, and inherited or acquired constitution, acted upon by the variable influences of climate, oc cupation, and habits of life, and still further modified in disease by the treatment and re gimen which may happen to be adopted. In consequence of the number and diversity of the influences brought to bear upon it, the human frame presents an object of study only less difficult than the human mind, affected by a like number and variety of moral causes, of which the true nature and force have to be unravelled by multiplied observations on the condition of mankind under different cir cumstances ; the aggregate of such observ ations constituting a great part of the science of statistics properly so called, and bearing to the practical science of government the same relation which pathology and therapeutics, based upon large collections of facts, do to the practice of medicine.
Now this dependence of the individual facts or events with which physiology and medicine are conversant on the concurrent action of a multitude of causes, has been urged as an ob jection to the introduction of the numerical method into the service of those sciences. It is admitted, that the use of numbers and averages by the astronomer who deals with the more simple relations of matter, such as magnitude and relative position, and by the engineer who avails himself of its more simple properties, such as its hardness, tenacity and elasticity, have contributed to make the science of the one perfect, and the art of the other safe ; but it is contended that the use of num bers cannot be extended beyond such narrow limits with safety or advantage, and that medi cine and political economy• lie beyond these limits. The actual practice of mankind, founded upon an instinctive perception of the necessity of employing figures in the service of the phy sician and statesman, may be fairly alleged as a sufficient answer to this objection ; but a little consideration will serve to show its futility.
In the first place, it is self-evident that the exclusion of figures from the service of medi cine, does not bring about the disuse of those very facts and events which are objected to as unfit to be employed as statistical or numerical elements. The physician will still persist in stating and recording the results of his expe rience. He will still assert that he has sometimes observed this symptom in a certain disease, that he has often found that remedy beneficial, that he has almost never known such and such a mode of treatment to fail. Those who con tend for the use of numbers in medicine, merely insist on the necessity of reducing the sometimes, the often, and the almost never to a more correct and intelligible form of expres sion ; and they argue that it is utterly incon sistent to object to the use of facts as mate rials or elements of numerical propositions, and yet not to censure the use of these same facts as foundations for loose and inaccurate verbal statements. From this dilemma there is obviously no escape. But, though the ob jection itself is futile, the misgiving of which it is the exaggerated expression is natural and well founded. It cannot excite surprise that the individual facts or events which own so many concurrent causes should be regarded as requiring, on the part of the observer, a greater degree of care in verifying, recording, collecting, and arranging them than would be necessary in the more simple cases already adduced ; and that both the facts themselves, and the numerical' expressions in which they are embodied, should be viewed with a pro portionate degree of distrust. From this mo derate and reasonable view of the case, no advocate of the numerical method will be found to dissent. On the contrary, he will seek to strengthen it by giving due promi nence to each separate ground of misgiving, and by laying down stringent rules for the guidance and governance of the observer. Before proceeding to detail some of these rules, it may be well to advert to a probable, and, indeed, obvious cause, of the distrust with which numerical data are sometimes regarded.