The numerical or statistical method may be defined as the science which prescribes rules for the bringing together of scattered observ ations, arranging them in classes, testing their sufficiency in point of number, and deducing from them, when so arranged, average and extreme results, fitted by their very condensa tion to become standards of comparison and data for reasoning.
The numerical method*, so defined and appear that a counter experience of the same kind was continually leading to its disuse. Thus Morgagni tells us that, when he was quite a young man and went to Bologna, both methods of using mercury, internal and ex ternal, were so far deserted, that he never saw any physician make use of them, or ever heard of his using them, for the whole space of eight years, during which he studied there.* It would also appear that from the beginning of the sixteenth century up to the present time, there has always been a large number of sur geons, who have either abandoned the mer curial treatment altogether, or have restricted the use of the mineral to certain exceptional cases.f In the difference of opinion which prevailed upon this subject, the necessity of submitting the question at issue to the test of figures made itself so strongly felt, that a series of the most elaborate inquiries was undertaken at the instigation of governments, or by private individuals. These inquiries resulted in the collection of nearly 80,000 facts, by means of which the possibility of promptly healing ve nereal sores without mercury and with but risk of a relapse, or of the occurrence of secondary symptoms, was conclusively esta blished.t To this same test of figures, all the questions which arise from time to time, as to the relative value of the several remedies recom mended in the treatment of syphilis are, by common consent, submitted. A most con vincing proof that the numerical method is, in all cases of doubt and difficulty, the means of solution to which men naturally resort, is af forded by the treatise of Benjamin Bell, on this very subject, published in the year 1793.§ Speaking of the treatment of incipient chancres by caustic, he notices the very important ob jection, that the cure of the sores was often succeeded by buboes ; and he adds, that for a considerable time he was induced to suppose that the swellings of the glands, which thus take place after the cure of chancres, were more the effect of accident than of the method of treatment, and that they would have oc curred tinder whatever management the sores might have been. The frequency, however,
of their appearance, led him at last to suspect that he was mistaken, and further observation made it obvious that this was the case. Ile goes on to observe, " As experiment alone could determine the question, I was resolved to employ this test. Of the first twenty patients who occurred with incipient chancres, in ten they were destroyed by an immediate and effectual application of lunar caustic, the remedy being employed, according to my usual custom at that time, instantly on my being called ; of the other ten, five were dressed with blue mercurial ointment, and five with common wax ointment. The sores to which caustic understood, comprises two distinct inquiries, the one relating to the individual facts which form the materials for the calculation of aver age and extreme values, and the other re ferring to the averages and extremes them selves. This natural and convenient division of the subject it is proposed now to adopt.
1. Offacts considered as the elements of sta tistical inquiries.— Scientific inquiries are con versant with two orders of facts :— namely, phenomena of varying intensity, and events brought about by a multitude of causes. The first class of facts enters very largely into the science of physiology ; the last class consti tutes, though not to the exclusion of the first, the mass of the materials by which the prac tical sciences of medicine and hygiene are built up.
As examples of phenomena of varying inten sity may be cited the pulse and respiration, the temperature of the body, the secretions of the skin, kidneys, and lungs, the evacuations of the bowels, the weight and stature of the body at different ages, and the muscular de velopment and power of different nations and classes of persons. These phenomena, care fully observed and recorded by the aid of the watch, the thermometer, the measure, the balance, and other instruments adapted to special purposes, become so many numerical values, having the same relation to the aver ages deduced from them, as the more simple events expressed in units bear to the mean results for which they furnish the materials.