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depth of the pit amounted to about 24 or 25 feet. It was by working out the slate-stone, that this bone was discovered sticking to the roof of the pit, where the men were pursuing their work; and with a great deal of caution, and no less pains, they got it down entire, but attached to a large piece of stone.

There was no water in the works, but such as descended from the surface through perpendicular fissures; and the whole was spent in forming the stalac tites and stalagmites, of which there was great variety, and constantly increasing of dimensions. One of the workmen had been so curious, as to mark the time. of the growth of some of them for several years past.

LXIX. On the Usefulness of Inoculation of the Horned Cattle to prevent the Contagious Distemper among them. By Dan. Pet. Layard, M. D., F. R. S. p. 528.

In this paper Dr. L. endeavours to prove that the contagious distemper which raged among the horned cattle of this country and France in 1745, 1746, 1747, and 1748, and other years, bore a great analogy to the small-pox, and that the cattle never take it a second time; in both which opinions he differs from the Marquis de Courtivron, author of 2 memoirs on this subject, read before the Royal Academy of Sciences at Paris. Hence he proposes inoculation, as the means of lessening the mortality of this distemper.

As to the nature, rise, progress, and fatality of this distemper at Issurtille, says Dr. L. it appeared to be the same disease as raged in these kingdoms. All the symptoms agreed as described by Rammazini, Lancisi, the Marquis de Courtivron, and in Dr. L.'s Essay. A distempered beast gave rise to the 3 infections. The illness was everywhere the same in Italy, France, and Britain; and either terminated fatally on the 4th or 5th day, when a scouring prevented the salutary eruptions, or in some cases by abortion; and on the 7th or 9th favourably, when the pustules had regularly taken their course. Though the Marquis did not observe, that any particular medicines were of use, he says, that in general acids were beneficial, especially poor thin wines somewhat sour; and that the distempered beasts were all fond of these acids. The fatality was likewise the same, as will appear from the Marquis's tables. cattle, 176 died. The mortality was chiefly among the fat cattle, or cows with calf, and young sucking or yearling calves; and of the surviving 16, only 2 calves out of 77 lived, and these 2, with 7 other beasts of the 16, escaped the infection, though constantly among the diseased.

Of 192 head of

The mortality was as considerable in these kingdoms. Whoever will compare the appearances, progress, and fatality of the small-pox, with what is remarked by authors of authority, as Rammazini and Lancisi, and other observers, relative to the contagious distemper among the horned cattle, will not be at a loss

one moment to determine, whether this disease be an eruptive fever, like the small-pox, or not.

Now if, as the Marquis has granted in both his memoirs, it be a general observation, that an eruption of pustules on some parts of the body, regularly thrown out, digested, and dried, was the means used by nature to effect the cure, and that in general the morbid matter did not affect the parotid, inguinal, or other glands, nor produce large carbuncles and abscesses, as the plague does: nay more, since it was observed by the Marquis, that the difference between the contagious distemper of 1745 and 1746, and of 1747 and 1748, was, that in the former the salutary eruptions appeared, but in the latter were, as he justly apprehended, checked by the excessive cold weather: and should it appear, that by inoculation the same regular eruptive fever had been produced, with every stage, and the same symptoms as arise in the small-pox; the nature of this distemper will then be ascertained. Dr. L. then proceeds to state the accounts he had received relative to the infection and inoculation of the cattle, and to offer some observations on the experiments made at Issurtille.

So long as the distemper had raged in Great Britain, not one attested proof had been brought of any beast having this disease regularly more than once. He made no doubt but these creatures might be liable to eruptions of different kinds; but as all sorts of eruptions, says Dr. Mead, are not the small-pox nor measles, so every pustule is not a sign of the plague. Through ignorance, or fraud, persons might have been deceived in purchasing cattle, and have lost them, as well in England as in the provinces of France mentioned by the Marquis; but until a second infection be proved, the general opinion must prevail in this case, as in the small-pox; for though many have insisted on the same thing with regard to the small-pox, yet a single instance, properly vouched and attested, had never been produced, either after recovery from the natural way, or from inoculation; unless what was frequently the case with nurses and others attending the smallpox, that is, pustules breaking out in their arms and face, be allowed as the signs of a second infection.

The farmers and graziers in Huntingdonshire, Cambridgeshire, Lincolnshire, Kent, and Yorkshire, whence Dr. L. had written testimonies, all agreed that they never knew of a beast having the contagious distemper more than once. In the first particularly, Mr. J. Mehew, the farmer mentioned in Dr. L.'s essay, had then among his stock at Godmanchester 8 cows, which had the contagious distemper the first time it appeared in Godmanchester in 1746. It * returned in 1749, 1755, and 1756; the 2 last not so generally over the town as the 2 former years. All these 4 times Mr. Mehew suffered by the loss of his cattle; yet those 8 cows, which recovered in 1746, remained all the while the distemper was in the farm the 3 years it raged, were in the midst of the sick

cattle, lay with them in the same barns, eat of the same fodder, nay of such as the distempered beasts had left and slabbered on, drank after them, and constantly received their breath and steams, without ever being in the least affected. Was not this a convincing proof? If in general the cattle be susceptible of a 2d infection, how came it, that not one of these 8 cows were affected?

In the years abovementioned the distemper spared no beast, but such as had recovered from that disease; and this was confirmed to Dr. L. by Mr. Mehew's father and brother, all the chief farmers of Godmanchester, and was the opinion of all the farmers and graziers in Huntingdonshire, who were so thoroughly convinced of there being no 2d infection, that they were always ready to give an advanced price for such cattle as had recovered from the contagious distemper. The Rev. Mr. Scaife, assistant to the Rev. Dr. Greene, Dean of Salisbury, in his parish of Cottenham, Cambridgeshire, acquainted Dr. L. that the farmers in that neighbourhood lost, in 1746 and 1747, 1200 head of cattle; in 1751 470; and told him that Messrs. Ivett, Sayers, Moor, Dent, Lawson, chief farmers at Cottenham, Messrs. Taylor, Sumpter, and Matthews, of his own parish of Histon, and the farmers of Wivelingham alias Willingham, unanimously declared they never had one instance of a beast having the distemper, twice. Mr. Thorpe, a farmer and grazier near Gainsborough in Lincolnshire, had had beasts recovered from the distemper, which had herded with cattle fallen ill afterwards, and never met with a single instance of a 2d infection. Mr. Loftic, an eminent surgeon at Canterbury, had inquired for Dr. L. of the farmers and graziers in that part of Kent, and about Romney-Marsh; and whence no belief of a 2d infection can be had. The Rev. Dr. Fountayne, Dean of York, wrote to him, that no beast had been known, in his neighbourhood, to have the distemper twice. And several persons from that county, and others, had told him the same thing.

If the above testimony of persons of character and veracity, together with the concurrent persuasion of farmers in general be allowed of, it must be determined, that there is no instance of a 2d infection. Supposing now it should appear that this distemper is regularly, as in the natural way, though in a milder manner, produced by inoculation, and that inoculation secures a beast also from a 2d infection; then undoubtedly inoculation will be recommendable. The very few trials made in England, and those not with the greatest exactness or propriety, will yet serve to put this matter out of all doubt. The Rev. Dean of York had 5 beasts inoculated, by means of a skein of cotton dipped in the matter, and passed through a hole like a seaton in the dew-lap. Of these 5, one cow near the time of calving died: the other 4 after going through the several stages of this contagious disease recovered; 2 of which being cows young with calf, did not slip their calves. All 4 herded with distempered cattle a long while, and

never had the least symptom of a 2d infection. Mr. Bewley, a surgeon of reputation in Lincolnshire, inoculated 3 beasts 2 years old, for Mr. Wigglesworth of Manton, in the dew-lap, and with mucus from the nostrils. All 3 had the regular symptoms of the contagious distemper in a mild manner, recovered, and though they herded a 12 month after with 5 or 6 distempered beasts, they never were the least affected. Mr. Bewley also declared to Mr. Thorpe, that there never was one instance produced that he knew of, of a 2d infection.

Since it was plain, that notwithstanding neither well-digested pus was made use of, nor incisions made in the properest places, and it might be supposed few medicines were given; yet inoculation succeeded so as to bring on the distemper in a regular and mild nanner, as "ppeared by the cows with calf not slipping their calves; one might fairly conclude, that in this contagious distemper, like the small-pox, the practice of inoculation was not only warrantable but much to be recommended.

But how came it then, that neither by application, digestion, nor inoculation, the distemper was not communicated in France? The Marquis says, that this distemper was not communicated but from one beast to another immediately. Dr. L. begged leave to say, that to his knowledge the distemper in February 1756 was carried from the farm yard, where he visited some distempered cattle, to 2 other farm yards, each at a considerable distance, without any communication of the cattle with each other, and merely by the means of servants going to and fro, or of dogs. The experiments made on 4 beasts, by tying over their heads part of distempered hides, or pieces of linen and woollen cloth or silk, which had received the breath and steams of dying cattle, serve to show, by the bullock's forcing off the cloth tied about him, that the putrid stench was disagreeable to him; but that neither his blood nor that of the other 3 beasts, was then in a state to receive the infection.

With regard to the pustules, which the Marquis relates were mixed with oats and bran, or dissolved in white wine; the distempered bile, which was mixed with milk; milk taken from diseased cows; water, in which part of a distempered hide had been steeped ; and the precaution taken to force these mixtures into the paunch of calves by means of a funnel, whose end was covered with a piece of raw distempered skin, that the beast might both swallow and suck in the disease; all these experiments could have no other effect than what followed; which was, that the acrimony of the distempered bile created first a nausea, and then produced a violent scouring, which killed the beast, leaving marks of its irritation on the intestines.

The practice of inoculation was but lately followed, and even now but little known in the provinces of France. Its advantages had not long since been strangely disputed at Paris. In the case of inoculating cattle, instead of a slip of




raw hide taken from a beast just dead, or putting a pustule into the neck, they should either have passed in the dewlap cotton or silk dipped in well digested pus, or have inserted in proper incisions cotton-thread or silk soaked with pus, either on the shoulders or buttocks; the true way of inoculating in the English manner. Some persons have indeed thought, that to inoculate with the blood of the infected would answer the intention; but most of the modern practitioners chuse to depend on digested matter.

Several constitutions would not receive infection, though inoculated ever so judiciously. A Ranby, a Hawkins, a Middleton, and other inoculators, would tell us that the incisions had sometimes suppurated much, and pustules had appeared round the edges of the wound without any other particular marks of the disease; and yet the patient had never had the small-pox afterwards. The Marquis mentioned an instance somewhat of the same kind in his first Memoir, p. 147.

LXX. Trigonometry Abridged. By the Rev. Patrick Murdoch, A.M., F.R.S. p. 538.

The cases in trigonometry, that can properly be called different from one another, are no more than 4; which may be resolved by 3 general rules or theorems, expressed in the sines of arcs only; using the supplemental triangle as there is


Case 1. When of three given parts two stand opposite to each other, and the third stands opposite to the part required. Then,

Theorem 1. The sines of the sides are proportional to the sines of angles opposite to them.

Cases 2 and 3. When the three parts are of the same name. And, when two given parts include between them a given part of a different name, the part required standing opposite to this middle part. Then,

Theorem 2. Let s and s be the sines of two sides of a spherical triangle, d the sine of half the difference of the same sides, a the sine of half the included angle, b the sine of half the base; and writing unity for the radius, we have ssa2 + ď b2 = 0; in which a or b may be made the unknown quantity, as the case


Note. 1. If this, or the preceding, be applied to a plane triangle, the sines of the sides become the sides themselves; the triangle being conceived to lie in the surface of a sphere greater than any that can be assigned.

Note 2. If the two sides be equal, d vanishing, the operation is shorter: as it also is when one or both sides are quadrants.

Note 3. By comparing this proposition with that of the Lord Napier, which

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