commonly called; nor is it indeed ftrially true in any elliptic orbit; but it may properly be confidered as an useful approximation in orbits that are nearly circular.

Memoir VIII. treats of the motion of a body in a spherical furface; in which it is retained by fome force urging it towards the center of the fphere, while it is continually impelled by fome other force, or forces, to change its direction in that furface. In this Memoir are laid down, in the most general form, the direction and quantity of the forces necessary to the continuance of fuch a compounded motion, the theorems being general for any kind of a path on the furface of the sphere. The learned author then illuftrates these general rules by an application to particular cafes, fhewing what kind of a curve will result from certain relations affumed between the forces, as also what must be the nature of the forces to cause the body to describe a given curve on the spherical furface, either a great or little circle, a loxodromic, or any other fpiral. Among thefe particular examples, he mentions fome cafes that had been treated as feparate problems by former eminent mathematicians, whom he fometimes animadverts upon in a free, but genteel manner, for certain little incorrectneffes, which it appears the greatest of them are not entirely exempt from. One of thefe examples is relative to the motion of a body in such a path on the spherical furface, that it fhall always be found in the circumference of a great circle of the sphere, while the plane of that circle itself revolves about one of its diameters as an axis. This being a cafe of confiderable importance, as relating to fome nice points in phyfical aftronomy, it has engaged the attention of most eminent writers on this difficult branch of phyfics; and among these the late excellent Mr. Thomas Simpson, in his Miscellaneous Tracts, on which our author observes, that he (Simpson) had computed the value of the force g (acting on the body in a direction perpendicular to the plane of the revolving circle) upon the fuppofition that, if u (the angular velocity of the revolving circle) be invariable, (the velocity of the body in the circumference of the circle) will likewise be fo; without taking any notice that will not be invariable when u is fo, unless the body be acted on, in the direction of the circumference of

the circle, by a force f

8=

2 v u Vry

as well as by the force

where is the fine of the distance of the

body from one of the poles of the revolving circle, to the radius r of the sphere. Indeed Mr. Simpfon has confidered the velocity as very fmall; and in that cafe it is true that the

force

force f will alfo be very fmall, but not abfolutely nothing, nor yet indefinitely fmall; for u (though fmall) being finite, the value of ƒ will also be finite. Mr. de la Lande, in his Aftronomy (art. 3547), propofing to explain Mr. Simpfon's computation, has obferved, that if only the force g act on the body,

will not be invariable when u is fo. But, without computing the requifite force f, or the exact value of the force g when f is equal to nothing, he neglects a part of the force g, and entirely omits the force f, as being what he calls infiniments petits du troifieme ordre; whereas they are not generally infiniments petits of any order whatever, but are indeed affignable quantities which may in fome cafes be confiderable, and therefore hould not be neglected without first computing their values, and fhewing that they really are inconfiderable in the cafe in question.

Memoir IX. and last, is relative to the motion of bodies in any variable plane whatever, that revolyes with an angular velocity about a line fituated in that plane. Here, as ufual, geBeral theorems are first investigated, that exprefs the relations between the feveral forces and certain lines drawn in and about the revolving plane, and from which any particular cafe is easily folved. Some examples of these cafes are here also given, fuch as when the revolving plane generates a cone, a paraboloid, &c. It is alfo remarked, that, as the preceding Memoir is only a particular cafe of this, namely, in which the revolving plane. generates a fphere, the theorems in it might be deduced from those in this.

Concerning the feventh, eighth, and ninth Memoirs, it may be obferved, that the common doctrine of centripetal forces comprehends only a part of what is neceffary to be understood in order to determine in general the path of a projectile, and its motion in that path, from a knowlege of its velocity and direction at any time, and of the force or forces acting on it whilft in motion;-there being innumerable cafes in which fuch force or forces may not continually urge the body towards a certain center, as the faid common doctrine fuppofes. The deficiency of that doctrine, in the books published relative to this fubject, the author has fupplied in the three memoirs above mentioned. And, as a farther application of the principal theorems in thofe memoirs may be requifite to explain, in a fufficient manner, the general doctrine of a projectile's motion, Mr. Landen gives us reafon to hope that he will make fuch application in fome fubfequent Memoirs, refpecting propofitions too intricate to be confidered in the examples which he thought proper to be given in the Memoirs themselves, where thofe principal theorems are investigated.

To promote the defign of the work, both in the volume before us, and in thofe which the author defigns to give hereafter, he has fubjoined to this an Appendix, confifting of the moft complete and extenfive tables for finding fluents that have ever been given to the public. These are divided into 16 claffes, containing almost 400 theorems, or formulæ of fluxions and fluents, for the moft part of the author's own invention; fome few only, that had been published by other writers, are inferted to make the fet more complete.

Philofophical Tranfactions, of the Royal Society of London, Vol. LXIX. For the Year 1779. Part II. 4to. 75. 6d. ferved. L. Davis.

THIS

"HIS Part begins with Article XXII. containing an Account of the Manner in which the Ruffians treat Perfons affected by the Fumes of burning Charcoal, and other Effluvia of the fame Nature. In a Letter from Matthew Guthrie, M.D. to Dr, Priestley. On this subject Dr. Guthrie gives the following information:

• People of condition in this country have double windows to their houses in winter; but the commoner fort have only fingle ones, which is the reason that, during a fevere froft, there is an incruftation formed upon the infides of the glass windows. This feems to be compofed of condenfed breath, perfpiration, &c. as a number of people live and fleep in the fame fmall room, efpecially in great cities. This excrementitious cruft is farther impregnated with the phlogiston of candles, and of the oven with which the chamber is heated.

When a thaw fucceeds a hard froft of long duration, and this plate of ice is converted into water, there is a principle fet loose, which produces all the terrible effects upon the human body, which the principle emitted from charcoal is fo well known to do in this country, where people every day fuffer from it. However, the Ruffians conftantly lay the blame upon the oven, when they are affected by the thawing of the cruft, as the effects are perfectly fimilar, and they cannot bring themselves to believe, that the diffolving of fo fmall a portion of ice can be attended with any bad confequence, when they daily melt larger maffes without danger: yet the oven does not at all account for the complaints brought on at this period; for, upon examination, they generally find every thing right there, and ftill the ugar, or hurtful vapour, remaining in the room.

As the effects of both are fimilar, as I have said above, and likewife the mode of recovery, I fhall only give you an account of the operation of the principle emitted by burning charcoal, and of the method of bringing those people to life who have been fuffocated by it (as I think it is erroneously termed): this will

fuperfede

fuperfede the neceffity of giving the history of both, or rather it will be giving both at the fame time.

Ruffian houfes are heated by the means of ovens; and the manner of heating them is as follows. A number of billets of wood are placed in the peech or ftove, and allowed to burn till they fall in a mafs of bright red cinders; then the vent above is fhut up, and likewife the door of the peech which opens into the room, in order to concentrate the heat; this makes the tiles of which the peech is compofed as hot as you defire, and fufficiently warms the apartment; but fometimes a fervant is fo negligent as to fhut up the peech or oven before the wood is fufficiently burnt, for the red cinders fhould be turned over from time to time to fee that no bit of wood remains of a blackish colour, but that the whole mafs is of a uniform glare (as if almoft tranfparent) before the openings are fhut, elfe the ugar or vapour is fure to fucceed to mifmanagement of this fort, and its effects are as follows.

If a perfon lays himself down to fleep in the room expofed to the influence of this vapour, he falls into fo found a fleep that it is difficult to awake him, but he feels (or is fenfible of) nothing. There is no fpafm excited in the trachea arteria or lungs to roufe him, nor does the breathing, by all accounts, feem to be particularly affected in fhort, there is no one fymptom of fuffocation; but towards the end of the catastrophe, a fort of groaning is heard by people in the next room, which brings them fometimes to the relief of the fufferer. If a perfon only fits down in the room, without intention to fleep, he is, after fome time, feized with a drowfinefs and inclination to vomit. However, this last symptom feldom affects a Ruffian, it is chiefly foreigners who are awaked to their dangers by a naufea; but the natives, in common with ftrangers, perceive a dull pain in their heads, and if they do not remove directly, which they are often too fleepy to do, are foon deprived of their fenfes and power of motion, infomuch, that if no perfon fortunately difcovers them within an hour after this worst stage, they are irrecoverably loft: for the Ruffians fay, that they do not fucceed in reftoring to life thofe who have lain more than an hour in a flate of infenfibility.

The recovery is always attempted, and often effected, in this manner. They carry the patient immediately out of doors, and lay him upon the fnow, with nothing on him but a fhirt and linen drawers. His ftomach and temples are then well rubbed with fnow, and cold water, or milk is poured down his throat. This friction is continued with fresh fnow until the livid hue, which the body had when brought out, is changed to its natural colour, and life renewed; then they cure the violent head ach which remains by binding on the forehead a cataplasm of black rye bread, and vinegar.

In this manner the unfortunate man is perfectly restored, without blowing up the lungs, as is neceffary in the cafe of drowned perfons; on the contrary, they begin to play of them

felves fo foon as the furcharge of phlogiston makes its efcape from the body.

It is well worthy of obfervation, how diametrically oppofite the modes are of reftoring to life, those who are deprived of it by water, and those who have loft it by the fumes of charcoal: the one confifting in the internal and external application of heat, and the other in that of cold. It may be alledged, that the ftimulus of the cold produces heat, and the fact seems to be confirmed by the Ruffian method of restoring circulation in a frozen limb by means of friction with fnow. But what is fingular in the cafe of people apparently deprived of life in the manner treated of is, that the body is much warmer when brought out of the room than at the inftant life is restored, and that they awake cold and fhivering. The colour of the body is also changed from a livid red to its natural complexion, which, together with fome other circumftances, would almoft lead one to fufpect, that they are restored to life by the fnow and cold water fome how or other freeing them from the load of phlogifton with which the fyllem feems to be replete; for although the first application of cold water to the human body produces heat, yet, if often repeated in a very cold atmosphere, it then cools inftead of continuing to heat, juft as the cold bath does when a person remains too long in it.'

Art. XXIII. An Account of an Apparatus applied to the equatorial Inftrument for correcting the Errors arifing from the Refraction in Altitude. By Mr. Peter Dollond, Optician. Communicated by the Aftronomer Royal.

Art. XXIV. Experiments and Obfervations on the inflammable Air breathed by various Animals. By the Abbé Fontana, Director of the Cabinet of Natural Hiftory belonging to his Royal Highnefs the Grand Duke of Tufcany.-Thefe experiments appear to have been undertaken with the view of afcertaining a difputed fact in natural philofophy. According to Dr. Prieftley's obfervations, inflammable air caufes the death of animals as readily as fixed air, and animals die convulfed in it. Mr, Sheele, on the contrary, maintains, that inflammable air not only does not kill the animals which breathe it, but that it is even innocent and good air. Mr. Sheele has himself breathed inflammable air contained in a bladder, without receiving any hurt.

Mr. Fontana began his enquiry with endeavouring to discover whether animals could bear inflammable air with impunity, when the receivers that contained it were immerfed in quickfilver. For this purpose, he introduced inflammable air, extracted both from zink and iron, by means of vitriolic acid, into various tubes filled with quickfilver, in which the air entered pretty free from moisture. He then introduced various

birds