however, who wish for farther information can have recourse to the writings of DE MOIVRE, J. BERNOUILLI, T. SIMPSON, &c. but particularly the former, who has not been surpassed by any other writer on this subject. Nevertheless, in addition to the problems given in page 465, one other should be noticed, as being one of the most important, as well as abstruse, in the whole theory of chance: it was first solved by Bernouilli, and afterwards to greater exactness by DE MOIVRE. The former introduces his solution of it with observing: "Hoc est illud problema, quod evulgandum hoc loco proposui, postquam jam par vicennium pressi, et cujus tum novitas, tum summa utilitas cum pari adjuncta difficultate omnibus reliquis hujus doctrinae capitibus pondus et pretium superaddere potest." Such, therefore, being the opinion of that eminent mathematician concerning this problem, perhaps the present additional note ought not to be concluded without giving the solution of it; more particularly as De MOIVRE, though he pursued the investigation to a greater degree of accuracy, has contented himself with stating the rules, without giving any demonstration of them. Proposition: Supposing a very great number of trials to be made concerning any event, it is required to determine the probability there is that the proportion of the number of times it will happen to the number of times it will fail in those trials will differ less than by very small assigned limits from the probability of its happening to the probability of its failing in a single trial. Solution:-Let the probabilities of happening and failing be equal, and the number of trials be n. Let Land L also be the two terms equally distant, by the interval l, from the middle term of the binomial 1 + 1)", and s the sum of the terms included between L and L, together with the extremes; then if n be a very great number, the probability that the event happens neither more fre 1 1 quently than n + 1, nor more rarely than n - I times will be 2 2 if the probability of its happening to the probability of its failing in any one trial be as a to b, let Land R be the two terms equally distant by the interval / from the greatest term of the binomial a + b)", and let S be the sum of the terms included between Land R, together with the extremes, then will the proba bility that the event happens neither more frequently than an a+b I times be rightly expressed by + 1 times, S a+b7 These are the rules given by DE MOIVRE for the solution of this very difficult proposition, which, he observes, are founded on the common principles of the doctrine of chances, and therefore require no demonstration. This is certainly true, so far as regards the general principles of the solution, but the method of determining the values of sand S are by no means so obvious. In this, indeed, consists the whole difficulty of the solution; and as DE MOIVRE has omitted the process by which he obtained those values, it will be necessary to supply the omission by inserting the following lemma, which is derived from SIMPSON'S treatise "On the nature and laws of chance." Lemma: To find the sum of the series 1 × 2 × 3 × 4 continued to z terms. Solution:-Let the series be = P, and its byp. log. =r-a.log. x + As +B++ &c. then will x + 1 - a. log. x + 1 + A. x + 1 + B C D Access denied; and over-head up grew Ibid. For TONN EFORT read ToURNEFORT. Page 135, 155. Dog. Among the eminent men Norfolk has given birth to, and one whose writings have an intimate connection with the animal now under annotation, we may mention JOHN KAYE, better known by his latinised name, Carus, a renowned doctor of physic in the reigns of Queens MARY and ELIZABETH, who was born at Norwich, 1510. His treatise de Canibus, or an account of the whole race of british dogs, was a masterly performance for the age in which it was written. It was composed at the request of his friend CONRAD GESNER; and established the fame of Dr. CATUS on the continent for his knowledge of natural history. In a progress of King JAMES I. to Cambridge, as he passed through Caius-College, which the doctor had founded, the master of that institution as a compliment to the monarch's learning, and also to the memory of the founder, presented KAYE'S History of the University to the king; upon which JAMES observed; "Give me rather CAIUS de Canibus." PENNANT selected this work out of all the publications extant on the subject, to illustrate his British Zoology, as the most judicious synoptical arrangement he could find. Like LINNAEUS, KAYE united a great variety of learning and science with the art of medicine. He died 1573; and was buried in the chapel of his own college, with this laconic inscription on his tomb:-" Fui CATUS. Vivit post funera virtus." The following diagram will serve to illustrate the genealogy of the canine race according to the system of BUFFON, so far curtailed, as only to exhibit the pedigree of such dogs that may be regarded as immediate descendants from the pastor, or shepherd-dog. Page 69, 70, 90, 115, 132, 162, 175. Verses as supposed to be written by ALEXANDER SELKIRE, during his solitary abode in the island of Juan Fernandez. I am monarch of all I survey, 1 disease possessing a totally different radical cause, not render man incapable of being affected with any other of those diseases which human nature is subject to? Or, why do small-pox, measles, scarlet-fever, and typhus-fever arise from and possess different radical causes? Or, why was smallpox never found to render mankind incapable of an attack from measles, or measles that of scarlet-fever? &c. (though all these belong to the same class of disease.) If, therefore, these as well as all other diseases with which we are acquainted, invariably produce their own likeness, cow-pox must, if it be a preventive of small-pox arise from and possess the same radical cause as small-pox itself: and let those who think otherwise prove, by those immutable laws which govern all productions, that nature ever varied lower than the first stage of a inule. The qualities of different natures are known not to produce the same similitude. The diseases of animals, too, are known, when uncompounded with others, to be as distinct as their species. Therefore the idea of one genus of animals being subject to the diseases of another, must be fallacious; since it is contrary to all the known kno laws by which nature is invariably governed, and has been from all eternity: no contagious disease ever producing other than its own determined likeness. Should, therefore, hydrophobia be supposed to arise from a virus secreted by any rabid animal, does it not follow that it must be, either infectious or contagious? and, if so, why are the appearances dissimilar? Why should hydrophobia appear in man, and not madness, until produced by mental and bodily exhaustion? It appears from nature's laws, that, for the preservation and protection of one genus of animals from the diseases of another, they have each been furnished with a peculiar radical cause in the formation of their own compounded bodies, which renders one genus proper food for another, thereby tending to prevent the existence of putrefaction upon the face of the earth. Now if it should be said that the economy and formation of every genus of animals is not difierent, how will it be accounted for that the dog, and every other carnivorous animal is found capable of feeding upon the bodies of every other genus, when even in the highest state of putrefaction, and of converting those compounds formed during such state into compounds proper for the support of life; while, if the body were placed among living animals of its own class, it would, from those invariable laws in nature, find its own likeness produce the same preternatural state, and, finally the destruction of life? A most dreadful and convincing proof of this assertion arises out of the contemplation of the dysentery in mankind; it shews the existence of a peculiar radical cause even in the formation of every minute part of the compounded viscera of the human frame; for the compound is evolved and inhaled, like all other infectious disease; it circulates, and is repelled; producing not the smallest preternatural state in any part, from a want of affinity, until brought into the sphere of attraction of that particular part of the viscera in which the disease did originate. The reason is, the radical cause; it is different, and the disease not finding the same attractive, consequently cannot find a seat. Such demonstration is, sufficiently powerful to prove that the economy and formation of every genus of animals must be different. If, then, the dog, in a state of madness, is supposed to secrete a virus capable of affecting mankind and all other animals with a disease which will destroy life, does it not follow, that that disease must find its own likeness in them? And, must not the dog be again susceptible of it from being bitten by a carnivorous animal? Again, are not all infectious and contagious diseases equally capable of producing their likeness as well after death as before? And, again, is it not from the principle of chemical affinities alone, that all infectious and contagious diseases are cured or prevented? And is it not from the invariable and unchangeable appearances in nature's laws that we are enabled to ascertain and class diseases generally? And is it not from close attentions to such laws that the medical art has been of such utility to mankind? So long, therefore, as this disease continues to be speculatively treated without due attention to those general laws, so long will it remain a disgraceful reflection upon medical professors! All medicines called specifics or preventives must be looked on as quackeries, upon which no faith can possibly be placed. The Editor does not wish to lesson the weak support the afflicted must at present lean on, for his sole intention in submitting these opinions to the public eye, is the hope that they will tend to alleviate sufferings; and as he is persuaded that but few men can feel pleasure in deceiving, so is he convinced that the diseases of one genus of animals are probably not conveyed to another. The disease, therefore, in man supposed to arise from the bite of a mad dog, or any other rabid animal of the canine species, seems to be a mental affection, on which no bodily remedies ever had, or can have avail. -As a farther proof of this, the numerous recorded cases furnish this evidence, that fewer deaths have occurred where medicines have not been administered; and it appears, from all analogical researches, not to have any existence in nature. Were medical professors, therefore, to endeavour to dispossess the mind of fear, and encourage a confidence in the means pursued, it would establish a mode of cure by which those too generally received (prejudiced) opinions would be put to flight; but should fear again resume the place of confidence, debility and death are generally inevitable. Notwithstanding such is the leaning of the Editor's mind, upon a subject which may justly be deemed of national importance; and which he here submits to the reader in the fond hope of contributing to calm the mind of the afflicted, to satisfy the scruples of the sceptic, and, if possible to diffuse general comfort and consolation, yet he will not reject from the pages of a book (which, perhaps, like its hero, may visit the four quarters of the globe) those prescriptions for the treatment of hydrophobia which have been handed down to us by the wisdom or experience of our ancestors. The following have been found, by the Editor, among some family papers : 1. A recipe for the bite of a mad dog, taken some years ago out of Calthorp church, Lincolnshire, the whole town being bitten by a mad dog, and all that took this medicine did well, while all the rest died mad. In a P.S. it is added: many years experience have proved that this is an effectual cure:-" Take leaves of rue, picked from the stalks and bruised, six ounces: garlic, picked from the stalks and bruised, Venice treacle or mithridate, and scrapings of pewter, of each four ounces. Boil all these over a slow fire in two quarts of strong ale, till one pint is consumed; then keep it in bottles, close stopped, and give of it, nine spoon-fuls to man or woman, warm, every morning for seven together, fasting. This, if given within nine days after the biting of the dog, will prevent the hydrophobia. Apply some of the ingredients from which the liquor was strained to the bitten place." 2. The Tonquin Recipe for the Bite of a Mad Dog. " Mix the above dose in three spoonfuls of arrack, brandy, or spirits of wine : |