EXAMPLE. • In 6000 Julian years, 24 days, 4 hours, 59 minutes, 52 feconds, Qu. How many mean lunations? This fhort method may be useful in many other cafes; but, as yet, I have only applied it to two. The first of which is, to find the number of troy pounds contained in any given number of avoirdupoise pounds, and the reverfe. The fecond is to find the quantity and weight of water that would fill an upright pipe of any given diameter and height: and confequently, to know what power would be required to work a common pump, or any other hydraulic engine, when the diameter of the bore of the pump, and the height to which the water is to be raised, are given; proper allowance being made for friction'. We have omitted the examples Mr. Ferguson has given of thefe two cafes, as they may be very eafily fupplied by the Reader, if he should be inclined to purfue this method. IV. A Recommendation of Hadley's Quadrant for Surveying, ef pecially the furveying of Harbours, together with a particular Application of it to fome cafes of Pilotage. By the Rev. John Michell, F. R. S. Among all the inftruments hitherto invented for making obfervations at fea, none are comparable to Hadley's quadrant; because the motion of the veffel has no fenfible effect in leffening the accuracy of the obfervation, and which is very greatly affected when taken with any other inftrument. Nor is it confined to taking altitudes, it has been often applied to the menfuration of angles in furveying; but Mr. Michell is the first we have feen, who has applied it particularly to the surveying of harbours, in which that peculiar property of not being affected by the motion of the veffel, gives it a very great advantage over all others. Mr. Michell has alfo very happily adapted that well known property of the circle, viz. That angles in the fame "fegment are equal to each other," to furveys of harbours, by which means, the precife fituation of the fhip may at any time be determined with fufficient accuracy. But as our Authors method for obtaining this useful acquifition cannot be explained without figures, we muft refer to the paper itself, where the the Reader will meet with full fatisfaction, and find some obfervations well worth his notice. V. A Letter from John Bevis, M. D. to the Rev. Dr. Birch; containing Aftronomical Obfervations, made at Vienna, by the Rev. Father Jofeph Liefganig. Thefe obfervations, which feem to be made with great care and circumfpection, relate to an occultation of the Virgin's Spike with the Moon, on the 20th of February; an eclipfe of the Moon on the 17th of March 1764; an eclipfe of the Sun on the 1st of April; another occultation of the Virgin's Spike with the Moon, on the 15th of April; all in the year 1764. VI. Two Theorems, by Edward Waring, M. A. Lucasian Profelor of Mathematics in the University of Cambridge, and F. R. S. These two theorems, which relate to the properties of lateral polygons infcribed in, and circumfcribed about, a given ellipfis, are deduced with remarkable elégance, and propriety. VII. A Differtation on the Nature of Evaporation and feveral Phanomena of Air, Water, and boiling Liquors: In a Letter from the Rev. Hugh Hamilton, D. D. F. R. S. Professor of Natural Philofophy in the Univerfity of Dublin. Few phænomena have given philofophers more trouble to account for, than the evaporation of fluids, and the afcent of watery vapours. Nieuwentyt was perfuaded that the particles. of fire, by adhering to thofe of water, formed moleculæ, fuperficially lighter than air. Halley thought that by the action of heat, the particles of water were formed into hollow spherules, filled with a finer air highly rarified, fo as to become specifically lighter than the external air. Defaguliers fuppofed the cause of the afcent of aqueous vapours was their being turned into an elaftic fteam, and always rarified more than the air, by the degrees of heat, to which bodies are usually fubject in the different seasons of the year. Lately another caufe has been affigned, namely, electricity. But none of these being fatisfactory, Dr. Hamilton has attempted to account for thefe phænomena on another principle, viz. that of folution; and fhewn, from a variety of experiments, that what we call evaporation, is nothing more than a gradual folution of water in air, produced and fupported by the fame means, namely, attraction, heat, and motion, by which other folutions are affected. In order to prove this, our Author firft confiders the nature of folution in general; and that, there really is the fame mutual attraction between the particles of water and air, as between the particles of any two bodies, one of which diffolves the other. This he proves from two experiments made by the accurate Boerhave, from whence it appears that all waters contain a confiderable quantity of elaftic air; and, confequently, Cc 2 that that this air must be retained in the fluid by the mutual attraction between their particles; for otherwife fo light and elastic a body as air would always afcend to the furface and escape. On the contrary, it is well known that the air, even in the drieft feafons, contains a large quantity of water. For dry falt of tartar will foon become fluid by the moisture it attracts from the air. But in order to corroborate this truth, and establish the principle in the moft fatisfactory manner, our Author proceeds to compare the properties of common folutions with thofe of evaporation in a great variety of inftances; whence it appears that folution and evaporation exactly agree in their feveral appearances, properties, and effects: A very fufficient reafon for concluding that they are natural operations of the fame kind; and that what we call evaporation, is nothing more than a gradual folution of water in air. Having thus eftablished the principle firft laid down, Mr. Hamilton proceeds to account for feveral phenomena of the atmofphere on that principle. The lowest part of the air being preffed by the weight of the atmofphere against the furface of the water, and continually rubbing upon it by its motion, has thereby an opportunity of attracting and diffolving thofe particles with which it is in contact, and feparating them from the reft of the water. And fince the caufe of folution, in this cafe is the ftronger attraction of the particles of water towards air, than towards each other, thofe that are already diffolved, and taken up, will be fill further raifed by the attraction of the dry air that lies over them, and thus will diffufe themfelves, ifing gradually higher and higher, and thereby leave the loweft air not fo much faturated, but that it will A¡N be able to diffolve, and take up fresh particles of water. And thus ice, or fnow, will evaporate as well as water, its particles being attracted and diffolved by the air, which is ftrongly preffed against its furface, for though heat promotes both folution and evaporation, yet we do not find that in either cafe any fenfible degree of it is abfolutely neceffary. In this manner will aqueous vapours afcend flowly into the atmofphere, even when we fuppofe the air almost at reft, for I believe it is never perfectly fo: but the folution of water in air, and the afcent of vapours, is greatly promoted by the motion of the winds, which bring freth and drier air into the place of that which may be already faturated and loaded with moisture, carrying it together with its moisture into the higher parts of the atmosphere, and difperfing it into all quarters. If we fhould now fuppofe the atmosphere to remain always of the fame temperature as to heat and cold, and to have always the fame density; when it was once faturated with water, all evaporation would cease, and the vapours already raised would always remain fufpended; for a fluid, while it continues of the fame temperature and denfity, will never let go the particles of a body that it has diffolved. We must, therefore, confider what are the caufes which occafion the air fometimes to part with the water it has diffolved, and which thereby keep up a continual circulation circulation of vapours. And thefe I fhall fhew to be the frequent viciffitudes of heat and cold, condensation, and rarefaction, to which the atmosphere is fubject. As to the effects of heat and cold, I have already hewn that the former promotes, and the latter checks, or in fome measure hinders evaporation, as well as other folutions; of which I gave an inftance in the vapours that are fufpended in the heat of the day, and by the cold of the night are precipitated, and fuffered to coalefce into drops of dew. From the fnowhat lies fo long on the tops of mountains, and from the experience of those who have paffed over them, we find that the higher parts of the atmosphere are much colder than the lower. Now, though vapours are first raised, and abound most in the lower parts of the atmosphere, yet they cannot there form themselves into clouds, because the heat that helped to diffolve them helps alfo to keep them diffolved. But when they are carried by the winds into the higher parts, where the fame heat is wanting, the cold air will not be able to keep diffolved all that are carried up, but must fuffer fome of them to coalefce into fmall particles, which flightly attracting each other, and being intermix. ed with air will form clouds, having the very fame appearance with fleam, or fmoak, which alfo confitt of finally particles of water, mixed with air, and not yet diffolved in it. Thefe clouds, when first formed, will remain fufpended, though they confift of water as well as air, becaufe the weight of their particles will not be able to overcome the refiftance they must meet with in defcending through the air. For when bodies are diminished, their quantities of matter, to which their weights are proportional, decrease fafter, or in a greater ratio, than their furfaces, to which the refiftance they meet with is proportional; and therefore, in very fmall particles, this refiftance may become greater than their weight. The different heights at which clouds are formed, depend on the quantity of vapours carried up, and the degrees of heat in the upper parts of the atmosphere; for the vapours will always afcend, till they meet with air fo cold, or fo thin, that it is not able to keep diffolved all that comes up; hence clouds are generally higher in fummer than in winter. When clouds are much increased by a continued addition of vapours, and their particles are driven clofe together by the force of the winds, they will run into drops heavy enough to fall down in rain; fometimes the clouds are frozen before their particles are gathered into drops, and then fmall pieces of them, being condenfed and made heavier by the cold, fall down in thin flakes of now, which appear to be fragments of a frozen cloud. But if the particles be formed into drops before they are frozen, they fall down in bailftones. When the air is replete with vapours, and a cold breeze fprings up, which it often does from the fea, the folution of these vapours is checked and clouds are formed in the lower parts of the atmosphere, and compose what we call a mift or fog. This generally happens in a cold morning; but when the fun has been up for fome time, the warm air again diffolves thofe watery particles, and it frequently clears up. In a hot fummer's day, the air lying over wet marshy ground, is copiously faturated with aqueous vapours; but the air growing cooler after fun-fet, will not be able to keep all thofe vapours diffolved, but muft let fome part of them coalefce into very small vifible particles, Cc3 that that this air must be retained in the fluid by the mutual attraction between their particles; for otherwife fo light and elastic a body as air would always afcend to the furface and escape. On the contrary, it is well known that the air, even in the drieft feafons, contains a large quantity of water. For dry falt of tartar will foon become fluid by the moisture it attracts from the air. But in order to corroborate this truth, and etablish the principle in the moft fatisfactory manner, our Author proceeds to compare the properties of common folutions with thofe of evaporation in a great variety of inftances; whence it appears that folution and evaporation exactly agree in their feveral appearances, properties, and effects: A very fufficient reason for concluding that they are natural operations of the fame kind; and that what we call evaporation, is nothing more than a gradual folution of water in air. Having thus eftablished the principle firft laid down, Mr. Hamilton proceeds to account for feveral phenomena of the atmosphere on that principle. The lowest part of the air being preffed by the weight of the atmofphere against the furface of the water, and continually rubbing upon it by its motion, has thereby an opportunity of attracting and diffolving thofe particles with which it is in contact, and separating them from the reft of the water. And fince the caufe of folution, in this cafe is the ftronger attraction of the particles of water towards air, than towards each other, thofe that are already diffolved, and taken up, will be fill further raised by the attraction of the dry air that lies over them, and thus will diffufe themfelves, rifing gradually higher and higher, and thereby leave the loweft air not fo much faturated, but that it will f¡N be able to diffolve, and take up fresh particles of water. And thus ice, or fnow, will evaporate as well as water, its particles being attracted and diffolved by the air, which is ftrongly preffed against its furface, for though heat promotes both folution and evaporation, yet we do not find that in either cafe any fenfible degree of it is abfolutely neceffary. In this manner will aqueous vapours afcend flowly into the atmofphere, even when we fuppofe the air almost at reft, for I believe it is never perfectly fo: but the folution of water in air, and the afcent of vapours, is greatly promoted by the motion of the winds, which bring freth and drier air into the place of that which may be already faturated and loaded with moisture, carrying it together with its moisture into the higher parts of the atmofphere, and difperfing it into all quarters. If we thould now fuppofe the atmosphere to remain always of the fame temperature as to heat and cold, and to have always the fame denfity; when it was once faturated with water, all evaporation would cease, and the vapours already raised would always remain fufpended; for a fluid, while it continues of the fame temperature and denfity, will never let go the particles of a body that it has diffolved. We must, therefore, confider what are the caufes which occafion the air fometimes to part with the water it has diffolved, and which thereby keep up a continual circulation |