A Discourse of the Rule of the Decrease of the Height of the Mercury in the Barometer, According as Places are Elevated Above the Surface of the Earth, with an Attempt to Discover the True Reason of the Rising and Falling of the Mercury, upon Change of of Weather

Orbita quattuor Interiorum Satellitum Saturni cum Anuse omnium maxime dilucida conspicitur A Discourse of the Rule of the Decrease of the Height of the Mercury in the Barometer, according as Places are elevated above the Surface of the Earth, with an Attempt to discover the true Reason of the Rising and Falling of the Mercury, upon change of Weather. By EDM. HALLEY. The Elastick Property of the Air has been long since made out, by Experiments before the R. Society and elsewhere; and the Resistance of its Spring is found to be nearly equal to the Weight or Force that compresses it; as also, that the Spaces the same Air occupies, under differing Pressures are reciprocally as those Pressures: it has been shown likewise by undoubted Experiment, that the Specific Gravity of the Air near the Earth's Surface, to that of Water, was once as 1 to 840, again as 1 to 852, and a third time, in a very large Vessel holding ten Gallons, as 1 to 860; all which, considering the Difficulty of the Experiment agree well enough, the Mercury standing at all those times about 29 Inches; but by reason 'twas Summer Weather, and consequently the Air rarified when all these were tried, we may without sensible Error say in round Numbers, that the Barometer standing at 30 Inches, and in a mean state of Heat and Cold, the specific Gravity of the Air to Water, is as 1 to 800: By the like Trials the Weight of Mercury to Water, is as 13½ to 1, or very near it; so that the Weight of Mercury to Air, is as 10800 to 1, and a Cylinder of Air of 10800 Inches or 900 Feet, is equal to an Inch of Mercury; and were the Air of an equal Density like Water, the whole Atmosphere would be no more than 5, 1 Miles high, and in the Ascent of every 900 Feet the Barometer would sink an Inch. But the Expansion of the Air increasing in the same Proportion as the incumbent Weight of the Atmosphere decreases, that is, as the Mercury in the Barometer sinks, the upper Parts of the Air are much more rarified. rarified than the lower, and each Space answering to an Inch of Quicksilver grows greater and greater, so that the Atmosphere must be extended to a much greater Height. Now upon these Principles, to determine the Height of the Mercury at any assigned Height in the Air, and contra having the Height of the Mercury given, to find the Height of the Place where the Barometer stands, are Problems not more difficult than curious; and which I thus resolve. The Expansions of the Air being reciprocally as the Heights of the Mercury, it is evident, that by the help of the Curve of the Hyperbola and its Asymptotes the said Expansions may be expounded to any given Height of the Mercury: For by the 65th Prop. Lib. 2. Conic. Mydorgii, the Rectangles AB, CE, AKGE, ALDE, &c. (in Fig. 5.) are always equal, and consequently the Sides CB, GK, LD, &c. are reciprocally as the Sides AB, AK, AL, &c. If then the Lines AB, AK, AL, be supposed equal to the Heights of the Mercury, or the Pressures of the Atmosphere; the Lines CB, KG, LD, answering thereto, will be as the Expansions of the Air under those Pressures, or the Bulks that the same quantity of Air will occupy; which Expansions being taken infinitely many, and infinitely little, (according to the Method of Indivisibles) their Sum will give the Spaces of Air between the several Heights of the Barometer; that is to say, the Sum of all the Lines between CB and KG, or the Area CBKG, will be proportioned to the Distance or Space intercepted between the Levels of two Places in the Air, where the Mercury would stand at the Heights represented by the Lines AB, AK; so then the Spaces of the Air answering to equal Parts of Mercury in the Barometer, are as the Areas CBKG, GKLD, DLPM, &c. These Areas again are, by the Demonstration of Gregory of St. Vincent, proportionate to the Logarithms of the Numbers expressing the Rationes of AK to AB, of AL to AK, of AM to AL, &c. So then by the common Table of Logarithms, the Height of any Place in the Atmosphere, having having any assigned Height of the Mercury, may most easily be found: For the Line CB in the Hyperbola, whereof the Areas design the Tabular Logarithms, being $0.0144765$; 'twill be, as $0.0144765$, to the difference of the Logarithms of 30, and any other lesser Number, so 900 Feet or the Space answering to an Inch of Mercury, if the Air were equally press'd with 30 Inches of Mercury and every where alike, to the Height of the Barometer in the Air, where it will stand at that lesser Number of Inches: And by the Converse of this Proportion may the Height of the Mercury be found, having the Altitude of the Place given. From these Rules I derived the following Tables. | A Table shewing the Altitude to given Heights of the Mercury. | A Table shewing the Heights of the Mercury at given Altitudes. | |---|---| | **Inch.** | **Feet.** | **Feet.** | **Inch.** | | 30 | 0 | 0 | 30, 00 | | 29 | 915 | 1000 | 28, 91 | | 28 | 1862 | 2000 | 27, 86 | | 27 | 2844 | 3000 | 26, 85 | | 26 | 3863 | 4000 | 25, 87 | | 25 | 4922 | 5000 feet | 24, 93 | | 20 | 10947 | 1 mile | 24, 67 | | 15 | 18715 | 2 | 20, 29 | | 10 | 29662 | 3 | 16, 68 | | 5 | 48378 | 4 | 13, 72 | | 1 | 91831 | 5 | 11, 28 | | 0.5 | 110547 | 10 | 4, 24 | | 0.25 | 129262 | 15 | 1, 60 | | 0.1 | 29 mil. or 154000 | 20 | 0, 95 | | 0.01 | 41 mil. 216169 | 25 | 0, 23 | | 0.001 | 53 mil. 278338 | 30 | 0, 08 | | | | 40 | 0, 012 | Up- Upon these Suppositions it appears, that at the height of 41 miles, the Air is so rarified, as to take up 3000 times the space it occupies here, and at 53 miles high, it would be expanded above 30000 times; but 'tis probable that the utmost power of its spring cannot exert itself, to so great an extension, and that no part of the Atmosphere reaches above 45 miles from the surface of the Earth. This seems confirmed from the Observations of the Crepusculum, which is observed commonly to begin and end when the Sun is about 18 degrees below the Horizon; for supposing the Air to reflect light from its most rarified parts, and that as long as the Sun illuminates any of its Atoms, they are visible to an Eye not intercepted by the Curvity of the Earth, it will follow from Fig. 6. that the proportion of the height of the whole Air, to the Semidiameter of the Earth, is much about as 1 to 90, or as the excess of the Secant of about 8½ degrees to Radius: For if E be the Eye of the Observer, S a place where the Sun sets at the end of twilight in E, and the Arch ECS, or TCA be found 18 degrees, the excess of the Secant of half thereof ECH, would be the height of the Air, viz. GH: But the Beam of the Sun ASH, and the visual Ray EH do each of them suffer a Refraction of about 32 or 33 minutes, whereby being bent inwards from H towards G, the height of the Air need not be so great as if they went straight; and having from the Angle ECS taken the double Refraction of the Horizontal Ray, the half of the remainder will be 8½ degrees circiter, whose Secant being 10 111 it follows that as 10000 to 111, so the Semidiameter of the Earth supposed 4000 miles, to 44, 4 miles; which will be the height of the whole Air, if the places E, S, whose visible portions of the Atmosphere ERZH, and SHKB just touch one the other, be 18 degrees asunder. At this height the Air is expanded into above 3000 times the space it occupies here, and we have seen the Experience of condensing it into the 60th Part of the same Space, so that it should seem, that the Air is a Substance capable of being compressed into the 18000th Part of the Space it would naturally take up, when free from pressure: Now what texture or composition of Parts shall be capable of this great Expansion and Contraction, seems a very hard Question; and which, I suppose, is scarce sufficiently accounted for, by the comparing it to Wool, Cotton, and the like springy Bodies. Hitherto I have only considered the Air and Atmosphere, as one unaltered Body, as having constantly at the Earth's Surface the 360th part of the weight of Water, and being capable of Rarefaction and Condensation in infinitum; neither of which Hypotheses are rigidly true: for here in England 'tis notoriously known, that the weight of the whole Atmosphere is various, being counterpoised sometimes by 28½ inches of Mercury, and at other times by no less than 30½, so that the under Parts being pressed by about a 15th part less Weight, the specific gravity of the Air upon that Score will sometimes be a 15th part lighter than another; Besides Heat and Cold does very considerably dilate and contract the Air, and consequently alter its gravity, to which add the Mixture of Effluvia or Steams rising from almost all Bodies, which assimilating into the form of Air are kept suspended therein, as Salts dissolved in Liquors or Metals in corroding Menstrua, which Bodies being all of them very much heavier than Air, their Particles by their admixture must needs increase the weight of that Air they lie incorporated withal, after the same manner as melted Salts do augment the specific gravity of Water. The other consideration is, that the Rarefaction and Condensation of the Air is not precisely according to the Proportion here laid down; for tho' Experiment very nearly agrees thereto, as may be seen in the 58th Chapter of Mr. Hook's Micrographie, yet are the Condensations not possible beyond certain degrees; for being compressed into an 800th part of the Space it takes up here, its Consistence would be equally dense with that of Water, which yields not to any Force whatsoever, as hath been been found by several Experiments tried here, and at Florence, by the Academia del Cimento. Nor can the Rarefaction proceed in infinitum; for supposing the Spring whereby it dilates itself, occasioned by what texture of Parts you please, yet must there be a determinate magnitude of the natural state of each Particle, as we see it is in Wool, and the like, whose Bodies being compressible into a very small Space, have yet a determinate Bulk which they cannot exceed, when freed from all manner of Pressure. These Objections being true do disturb the Geometrical accuracy of these Conclusions, drawn from the specific Gravity of the Air observed at any time; but the Method here shewn will compute by a like Calculation, the Heights of the Quicksilver, and the Rarefactions of the Air from any assigned Height of the Barometer at the Earth's Surface, and any specific Gravity given. As to the Condensation and Rarefaction by Heat and Cold, and the various Mixture of Aqueous and other Vapours, these two Objections seem generally to compensate each other; for when the Air is rarified by Heat, the Vapours are raised most copiously, so that tho' the Air, properly so called, be expanded and consequently lighter, yet the Interstices thereof being crowded full of Vapours of much heavier Matters, bulk for bulk the weight of the Compositum may continue much the same; at least a most curious Experiment made by the ingenious Mr. John Casswell of Oxford upon the top of Snowdon-Hill in Caernarvonshire, seems to prove that the first Inches of Mercury have their portions of Air near enough to what I now determine; for the height of the Hill being 1240 Yards or very near it, he found the Mercury to have subsided to 25, 6 Inch. or 4 Inch. below the mean Altitude thereof at the Level of the Sea (which is a greater difference than has been found in any of our former Experiments,) and the Space answering to 4 Inch. by my Calculation should be 1288 Yards; and it agrees as well with the Observations in the Appendix to Mr. Pascal's Book, del' Equilibre des Liqueurs, Liqueurs, made on the high Hill in Auvergne, call'd le puy de Domme. So that the Rarefaction and Vapours seem not to have altered considerably the Gravity of the under Parts of the Air; and much above the height where these Experiments were made, do few Vapours ascend, and the Cold is such that the Snow lies continually, so that for the more elevated Parts of the Sphere of Air there is much less reason to doubt. But now we have had occasion to mention the difference there is between the height of the Mercury at one time, from the height thereof at another, it may not be unacceptable to offer at some Reasons for the said Difference, which, at least to myself, seem to have some appearance of Truth; first then, 'tis undoubtedly demonstrable, that the height of the Cylinder of Mercury, is equal to the weight of the whole incumbent Air, and consequently that that whole is sometimes a fifteenth more than at other times, which cannot otherwise be, but by the access of new Matter when 'tis heavy, and its diminution when 'tis light; that Hypothesis therefore that shews how the Air shall be increased or diminished, in any particular Place, will give a reason for the greater and lesser height of the Mercury in the Baroscope: but to direct us in the choice of the several Causes, which may be assigned for the increase and decrease of the Air, 'twill not be unnecessary to enumerate some of the principal Observations made upon the Barometer, most whereof are sufficiently known already to all those that are curious in these Matters. The first is, that in calm Weather, when the Air is inclined to Rain, the Mercury is commonly low. 2. That in Serene good settled Weather the Mercury is generally high. 3. That upon very great Winds, tho' they be not accompanied with Rain, the Mercury sinks lowest of all, with relation to the Point of the Compass the Wind blows upon. 4. That cæteris paribus the greatest heights of the Mercury are found upon Easterly and North-easterly Winds. 5. That in calm frosty Weather, the Mercury generally stands high. 6. That after very great Storms of Wind, when the Quicksilver has been low, it generally rises again very fast. 7. That the more Northerly Places have greater Alterations of the Baroscope than the more Southerly. 8. That within the Tropicks and near them, those accounts we have had from others, and my own Observation at St. Helena make very little or no Variation of the height of the Mercury in all Weathers: Now that Theory that can well account for all these Appearances, will in all Probability approach nearer the true Cause of the Barometers Variations, than any thing hitherto offered; and such an one I am bold to believe, is that which I here lay down, with Submission to better Judgments. I conceive that the principal Cause of the Rise and Fall of the Mercury, is from the variable Winds, which are found in the Temperate Zones, and whose great unconstancy here in England is most notorious: I shall not at present enquire into the Cause of its Uncertainty, but the Matter of Fact being most undoubted, the legitimate Consequences thereof must be allowed me; let it proceed from what it will. A Second Cause is the uncertain Exhalation and Precipitation of the Vapours, lodging in the Air, whereby it comes to be at one time much more crowded, than at another, and consequently heavier; but this latter in a great measure depends upon the former. Now from these Principles, I shall endeavour to Explicate the several Phenomena of the Barometer, taking them in the same Order I laid them down. 1. Why in calm Weather, the Air being inclined to Rain, the Mercury is commonly low? I answer, that the Mercury's being low, inclines it to Rain, for the Air being light, the Vapours are no longer supported thereby, being become specifically heavier than the Medium wherein they floated; so that they descend towards the Earth, and in their fall meeting with other aqueous Particles, they incorporate together and form little Drops of Rain; but the Mercury's being ing at one time lower than at another, is the effect of two contrary Winds blowing from the place where the Barometer stands; whereby the Air of that place is carried both ways from it, and consequently the incumbent Cylinder of Air is diminished, and accordingly the Mercury sinks; as for Instance, if in the German Ocean it should blow a Gale of Westerly Wind, and at the same time an Easterly Wind in the Irish Sea; or if in France it should blow a Southerly Wind, and in Scotland a Northern; it must be granted me that that part of the Atmosphere impendent over England, would thereby be exhausted and attenuated, and the Mercury would subside, and the Vapours which before floated in those parts of the Air of equal Gravity with themselves, would sink to the Earth. 2. Why in serene good settled Weather, the Mercury is generally high? To this I answer, That the greater height of the Barometer is occasioned by two contrary Winds blowing towards the place of Observation, whereby the Air of other places is brought thither and accumulated; so that the incumbent Cylinder of Air being increased both in height and weight, the Mercury pressed thereby must needs rise and stand high, as long as the Winds continue so to blow; and then the Air being specifically heavier, the Vapours are better kept suspended, so that they have no Inclination to precipitate and fall down in Drops, which is the reason of the serene and good Weather which attends the greater heights of the Mercury. 3. Why upon very great Winds or Storms, though accompanied with no Rain, the Mercury sinks lowest of all, with relation to the point of the Compass upon which the Wind blows? This is caused by the very rapid Motion of the Air in these Storms; for the Tract or Region of the Earth's Surface wherein these Winds rage, not extending all round the Globe, that stagnant Air which is left behind, as likewise that on the sides, cannot come in so fast as to supply the Evacuation made by so swift a Current, so that the Air must must necessarily be attenuated when and where the said Winds continue to blow, and that more or less according to their Violence; add to which that the Horizontal Motion of the Air being so quick as it is, may in all probability take off some part of the perpendicular Pressure thereof: and the great Agitation of its Particles, is the reason why the Vapours are dissipated and do not condense into Drops, so as to form Rain, otherwise the natural Consequence of the Air's Rarefaction. 4. Why caeteris paribus the Mercury stands highest upon an Easterly or North-easterly Wind. This happens because that in the great Atlantick Ocean on this side the 35th degree of North Latitude, the Westerly and South-Westerly Winds, blow almost always Trade, so that whenever here the Wind comes up at East and North-East, 'tis sure to be checked by a contrary Gale, as soon as it reaches the Ocean; wherefore according to what is made out in our second Remark, the Air must needs be heaped over this Island; and consequently the Mercury must stand high, as often as these Winds blow. This holds true in this Country, but is not a general Rule for others, where the Winds are under different Circumstances: and I have sometimes seen the Mercury here as low as 29 Inches, upon an Easterly Wind, but then it blew exceeding hard, and so comes to be accounted for by what was observed upon the 3d Remark. 5. Why in calm and frosty Weather the Mercury generally stands high? The Cause hereof is, as I conceive, that it seldom freezes but when the Winds come out of the Northern and North-Eastern Quarters, or at least, unless those Winds blow at no great distance off; for the Northern Parts of Germany, Denmark, Sweden, Norway, and all that tract from whence North-Eastern Winds come, are subject to almost continual Frost all the Winter; and thereby the lower Air is very much condensed, and in that State is brought hitherwards by those Winds, and being accumulated by the Opposition of the Westerly Wind blowing in the Ocean, the Mercury must must needs be prest to a more than ordinary height; and as a concurring Cause, the shrinking of the lower Parts of the Air into lesser room by Cold, must needs cause a Descent of the upper Parts of the Atmosphere to reduce the Cavity made by this Contraction to an Equilibrium. 6. Why after very great Storms of Wind, when the Mercury has been very low, it generally rises again very fast? This I have frequently observed, and once found it risen an Inch and half in less than six hours, after a long continued Storm of South-west Wind. This seems to be occasioned by the sudden accession of new Air to supply the great Evacuation which such continued Storms make thereof, in those places where they happen (as in the third Remark) and by the Recoil of the Air, after the Force ceases that impell'd it; and the reason why the Mercury rises so fast, is because the Air being very much rarified beyond its mean Density, the neighbouring Air runs in the more swiftly to bring it to an Equilibrium, as we see Water runs the faster for having a great Declivity. 7. Why in more Northerly Places the Variations of the Baroscope are greater than in the more Southerly? The Truth of the Matter of Fact is proved from Observations made at Clermont and Paris, compared with others, made at Stockholm, as may be seen in the Appendix to Mr. Pascal's Book, before cited. The Reason I conjecture to be, that the more Northerly Parts have usually greater Storms of Wind than the more Southerly, whereby the Mercury should sink lower, in that Extream; and then the Northerly Winds bringing the condensed and ponderous Air from the Neighbourhood of the Pole, and that again being checked by a Southerly Wind, at no great distance, and so heaped, must of necessity make the Mercury in such case stand higher in the other Extream. 8. And Lastly, Why near the Equinoctial, as at Barbadoes and St. Helena, there is very little or no Variation of the Height of the Barometer? This Remark, above all others, confirms the Hypothesis of the Variable Winds being the cause of these these Variations of the Height of the Mercury, for in the Places above-named, there is always an easy Gale of Wind blowing nearly upon the same Point, viz. E. N. E. at Barbadoes, and E. S. E. at St. Helena; so that there being no contrary Currents of the Air, to exhaust or accumulate it, the Atmosphere continues much in the same State: However upon Hurricanes, the most violent of Storms, the Mercury has been observed very low; but this is but for once in two or three Years, and it soon recovers its settled state of about 29½ Inches. I doubt not but the same thing is in the East Coast of Africa and in India, where the Monsoons or Winds are Trade for half the Year one way, and half the Year another; only 'tis probable, that there may something worth noting happen, about the Times of the Change or Shifting of the Winds, which might be obtained if any body had the Curiosity to keep the Barometer at our Factories in India. I doubt not but this Doctrine will find some Opposers, and that one principal Objection will be, That I suppose the Air sometimes to move from those Parts where it is already evacuated below the Equilibrium, and sometimes again towards those Parts, where it is condensed and crowded above the mean state, which may be thought contradictory to the Laws of Staticks and the Rules of the Equilibrium of Fluids. But those that shall consider how, when once an Impetus is given to a fluid Body, it is capable of mounting above its Level, and checking others that have a contrary Tendency to descend by their own Gravity, will no longer regard this as a material Obstacle; but will rather conclude, that the great Analogy there is between the rising and falling of the Water upon the Flux and Reflux of the Sea, and this of the accumulating and extenuating the Air, is a great Argument for the Truth of this Hypothesis. For as the Sea, overagainst the Coast of Essex, rises and swells by the meeting of the two contrary Tides of Flood, whereof the one comes from the S.W. along the Channel of England, and the other from the North; and on the contrary sinks below its Level upon the retreat of the Water both ways, in the Tide of Ebb; so it is very probable, that the Air may ebb and flow, after the same manner; but by reason of the diversity of Causes, whereby the Air may be set in moving, the times of these Fluxes and Refluxes thereof are purely casual and not reducible to any Rule, as are the Motions of the Sea, depending wholly upon the regular Course of the Moon. The next Transaction shall give an Historical Relation of those Winds which are found to have anything of Constancy, and shall endeavour to assign the Causes thereof. An Account of two Books, (1.) A Free Enquiry into the vulgarly received Notion of Nature, by the Honourable R. Boyle, Esq.; Printed by J. Taylor at the Globe in St. Paul's Church-Yard, Anno 1686. 8vo. 'TIS not without reason, that the renowned Author of this Treatise wonders that none have written concerning Nature herself, and yet so many have so largely treated of the Works of Nature. But this will seem less strange to him that considers for how many Ages the whole learned World has been devoted to the Peripatetick Principles of Matter and Form, and with how blind an Obedience the Doctrine of Aristotle hath been universally received and maintained: For the vulgar Notion of Nature concurring with the Peripatetick, having been generally admitted, all Men thought it unsafe to oppugn the Opinion of the Multitude, and at the same time to call in question the Authority of those reputed for Learning; subjecting their own Judgments, by a servile Resignation unworthy the Name of a Philosopher, to the Dogma's of others. This seems to be the chief, if not the only Cause of the Propaga-