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mentation, is multitudes of impreceptible animalcula floating in the atmosphere; that these are the caufe of all epidemical difeafes, but more particularly of the fmall-pox; that they return at particular seasons in greater or leffer numbers; that thefe bodies, imperceptible as they are to the human organs of vifion, imprison the most malignant tribes of the fallen angelic spirits.'

However abfurd and chimerical fuch an hypothesis must appear, the practice of the Bramins, from the more folid principles on which it is founded, and the general fuccess which attends it, deferves to be regarded as falutary and judicious: and the fimilarity, in point of cool regimen, of the method here delivered, to that which has been of late fo fuccessfully adopted in this kingdom, confers on the new plan of Inoculation the fanction of antiquity.

X. A Vindication of the new Method of Inoculating the Small-Pox, against the Arguments and Objections of Dr. Langton and Mr. Bromfield, wherein it is demonftrated, that the Distemper communicated by this Method is the genuine Small-Pox; that Patients fo inoculated are not in the leaft Danger of taking the Diftemper in the natural Way; and alfo that the Method itfelf bids fair, in the Hands of judicious Practitioners, to be come in the higheft Degree beneficial to Mankind: In which is comprehended an Inquiry into the true Causes, which render the Diftemper fo very favourable, in this Way of Inoculating. By Giles Watts, M. D. 8vo. Pr. 25. Johnson.

O much has of late been written concerning the new method of inoculation, that it might naturally be expected, the true merit of this practice should now be fully ascertained. But fuch is the variety in human conftitutions, and fo controvertible, in many cafes, the propriety of medical practice, that subjects of this fort are frequently of all others productive of the longest difputation. Rational practice and empiricifin appeal alike to the tribunal of experience; and the judgment, which ought to be fufpended, is either heated with the prejudice of party, or hurried away by popular opinion.

The first part of the treatife now before us is a vindication of the new method of inoculation, against the objections of Dr. Langton, the moft violent of its adverfaries who has appeared Min public. One argument infifted upon by that phyfician, in proof that the diforder communicated by the new inoculators is not the genuine fmall-pox was, that feveral patients had been *-inoculated by them three or four times. The author of this

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Effay acknowledges the fact; but affirms, that it was done merely for the fatisfaction of the patients, who had fuffered the

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disorder in fo flight a manner, that they could not think themfelves fecure from a future infection. · They do not even intimate (meaning the inoculators) that ever a fecond, third, or fourth inoculation has infected a patient of theirs with the finall-pox: much lefs, that any one ever took the diftemper, after inoculation, in the natural way. Indeed, it is notorious, that hardly ever either of these accidents have happened in the new way of inoculation. I myself will, on the strength of my own experience only, undertake to fay fuch accidents are extremely uncommon.' The conclufion I would draw from the premises is, that the above gentlemen acted very judiciously, in inoculating their patients feveral times, when they had the diftemper fo extremely lightly, not only to fatisfy them, that they had paffed through it, but also to take away all poffibility of a natural infection happening afterwards.'

It might be inferred from the last argument, that the inoculators themselves were not entirely fatisfied of their patients having actually paffed through the fmall pox. Such diffidence, however, in the infancy of a practice, cannot be conftrued, with certainty, into a consciousness of the infufficiency of the matter used for infection to produce the diforder. The smallpox has often been found extremely light, even in the natural manner nor is it determined by any experiment, in what degree the variolous disorder must exift, for fecurity from future infeЯtion ; nor what quantity of our fluids must neceffarily be facrificed, by affimilation, to the ferment of the disease.

Dr. Langton had obferved, that "in the inoculated, the pock being nothing but clear lymph, is foon re-abforpt by the cutaneous glands, and disappears in a few hours.” And he adds, "From this very fymptom it can be demonftrated, that the matter at prefent inoculated is by no means variolous." To this it is answered by the author: I have shewn above, that the pocks maturate in the inoculated in the new way, as they do in patients under the natural small-pox, Therefore, as to what he here fays of their being "reabforbed by the cu"taneous glands, and difappearing in a few hours," it is altogether without foundation, and contrary to the most notorious facts. And I will defy him to fhew the diftemper fo inoculated to be different from the natural fmall-pox, either in the maturation, exficcation, or even the defquamation of the pocks, or indeed in any other circumstance, the lightness only excepted.'

These are the moft material topics which we find among the author's remarks on the Effay of Dr. Langton. He next proceeds to the confideration of fome of the arguments and

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objections of Mr. Bromfield: among the principal of which is the following.

Mr. Bromfield fays, an inflamed ftate of the blood is certainly a great objection to the operation being done, as experience has long fince determined." I fcarcely know what Mr. Bromfield means by "an inflamed ftate of the blood." It feems to me a vague indeterminate kind of an expreffion. If he means a fizy ftate of it, I muft beg leave to diffent from him. I remember fome years ago a very judicious and experienced practitioner bled a patient under preparation for inoculation, and finding his blood very fizy, obferved on the occaflon, that he would probably have the diftemper very feverely. The event however fhewed he was mistaken in his prognoftick; the patient had the diftemper very lightly, indeed much more favourably, than any one of a large company who were inoculated with him. To fay the truth, in the prefent way of inoculation, the state of the blood is of little confequence, fo very powerful is the method pursued in it, in fubduing the diforder. If the vifcera are but found, and the health of the patient fufficiently good, to enable him to go through the dif cipline required, without its being impaired by it, it is fufficient. It is fcarce poffible for him under this method, unless it be his own fault, to fuffer much from the diftemper itself.

In this paffage we may obferve a remarkable inconfiftency. For, fhould it be granted, as the author afferts, that, in the new way of inoculation, the ftate of the blood is of little confequence, fo very powerful is the method pursued in it, in fubduing the diforder, it will follow, that the indifcriminate ufe of fuch a powerful method in all constitutions, must be extremely unwarrantable: and this, in our opinion, is the most material objection against the propriety of the new method of inoculation. The great points which ought to be determined, are, whether any of those who have been inoculated in this way, have taken the fmall-pox afterwards, in the natural manner or, whether fuch feem more liable to a fresh infection, than those who have been inoculated according to the former practice. When these facts are clearly afcertained, the argument of the too great mildness of the diforder, muft entirely vanish, and the rectitude of the whole preparatory and medicinal courfe be judged of, from the general iffue of the difeafe, and the alterations produced in particular conftitutions.

XI. A new and complete Treatife of Trigonometry; in which are contained the Orthographic, Analytical and Logarithmical Solutions of the feveral Cafes of Spherical Triangles, whether right angled or oblique, with Corollaries for plane Triangles; a comprehensive Theory of the Fluxions of fplerical and plane Triangles; and a Variety of curious and interefting Particulars, not to be met with in any orber Treatife upon this Subject, Carefully translated from the French of M. Mauduit. By W. Crakelt. 8vo. Pr. 4 s. Jerved, or 5's. bound in Ca'f. Turpin.

ERY few writers upon the fubject of trigonometry, have endeavoured to enlarge this ufeful branch of mathematical knowledge, by applying to their calculations the improved methods which, from time to time, have been discovered by help of the modern analyfis; they have, in general, contented themselves with giving directions for folving the cases of plane and spherical triangles by a logarithmical application of the common proportions, without attempting to extend their views beyond the difcoveries of their predeceffors. In this manner many have employed themselves, and, notwithstanding the number of books increased, yet scarce any effential progrefs was made; their labours ferved only to fill the world with multiplied comments upon originals, which in themselves were often either trifling or infignificant. On the other hand, by introducing the fluxionary calculus into the computations relating to the fides and angles of plane and spherical triangles, the bufinefs of trigonometry becomes greatly facilitated and im. proved; elegant and general theorems are readily obtained for fome of the most important difquifitions in aftronomy, fuch as determining the effect of parallax and refraction in obfervations made of the moon and other heavenly bodies, the nutation of the earth's axis, and preceffion of the equinoxial points, &c.

These confiderations induced M. Mauduit to compile the work now before us, wherein, by the application of algebra and the higher calculus, the principal properties of spherical triangles are investigated in a very curious and concise manner; but being chiefly analytical, fome may perhaps, as M. Mauduit himself obferves, confider it as a display of algebraical formulæ, entirely useless in a treatife of trigonometry: however, from fuch, continues our author, I fhall take the liberty of requesting a fufpenfion of judgment, at least till they have undertaken the ftudy of the different works of calculation relative to the theory of Newton for aftronomy is become fo excellent and delicate a science, that it is impoffible to have too many helps for facilitating the calculations it requires, and perfecting the feveral parts upon which it depends; and for thofe gentlemen

who have no intention of ftudying this fubject thoroughly, a perufal of the five or fix first theorems may be fufficient.'

With regard to the work itself, we think it a curious and elegant performance, worthy the perufal of mathematicians in general, but more especially of those who are defirous of being acquainted with the phyfical parts of astronomy; and Mr. Crakelt has (in our opinion) not only done juftice to the original, but likewise greatly enhanced its value, by the judicious annotations which he has interspersed throughout the translation.

MONTHLY CATALOGUE.

12. Letters of the Right Honourable Lady Jane Douglas; with feveral other important Pieces of private Correspondence. 8vo. Pr. 35. Wilkie.

THE

HE unaffected fimplicity, endearment, and tenderness, which breathe through thefe Letters, the authenticity of which cannot be difputed, are fo inimitable, that a reader of the smallest discernment may fafely pronounce them to be the undisguised effufions of a good heart. The cafual manner in which many of them were discovered (having been accidentally relieved, fome years after they were written, out of pawn, where they lay in an old cloak-bag, with Sir John Stewart's landlord in the Borough, when he had the liberties of the King's-Bench prison) is an additional proof that they were never intended for the inspection of any perfon, except that of the parties to whom they are addreffed. As they speak for themselves more powerfully than they can be recommended by any pen, we shall only defire, that the reader may fit down to the perufal of them with the fpirit of difinterestedness and impartiality. Could the following letters be indicted by a base impoftor, by a woman capable of obtruding a fpurious brood to reprefent, perhaps, in point of antiquity and eminence, the nobleft family in Europe which is not royal ?

Lady Jane Douglas to Mr. Stewart,

" Dear Mr. Stewart, Chelsea, Thursday, March 5. I have this moment the pleasure of your letter by your meffenger; this and all your's are ever welcome and agreeable to me; but the paragraph in fome of your late letters, and in this last one in particular, upon religious matters, abfolutely charm me go on, dear Mr. Stewart, fix your eyes, your hope, and truft above, and all worldly concerns will foon feem perfectly eafy, nay will, in reality, become fo; for God never

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