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rxpanded above 50,000 times : but it is probable, fays Dr. 

 Halky, that the utmoft power of its fpring cannot exert 

 itfelf to fo great an exteniion, and that no part of the atmo- 

 fphere reaches above 45 miles from the furface of the earth. 

 However, it follows from the principles above ilated, that 

 the air has a finite denlity at an iiitinite diftancc from the 

 centre of the earth, or fiich as would be reprefented by an 

 ordinate drawn through the centre. But at great diftances 

 its rarity would be fo great, that its reilftance would be in- 

 fenfible, though the retardation occafioncd by it has been 

 accumulated for age-s. At the moderate diftance of 5CO 

 miles, the rarity is fo great that a cubic inch of common 

 air expanded to that degree would occupy a fphere equal to 

 the orbit of Saturn ; and the whole retardation fuftaitied by 

 this planet, after fome millions of years, would not exceed 

 what would be occafioned by its meeting with one particle 

 of matter weighing half a grain. Hence it may be reafon- 

 ably inferred, that the vilible univerfe is occupied by air, 

 which, by its gravitation, will accumulate itfelf round every 

 Body in it, in a proportion depending on their refpeftive 

 quantities of matter ; the larger bodies attrafting more of 

 it than the fmall ones, and thus forming an atmofphere 

 about each. 



Dr. Hallev obferves, that as the weight of the atmo- 

 fphere is different at different times, its lower parts will be 

 unequally prcffed, and confequently its fpeciSc gravity will 

 be alfo variable. This variation he partly afcribes to the 

 effect of heat and cold, and alfo to the influence of other 

 caufes ; but he was of opi ion, that the condenfation and 

 rarefaftion, occafioned by colJ and heat, and by the 

 various mixtures of aqueous and other vapours, campen- 

 fate one another ; for he fays, that when the air is rare- 

 fied by beat, the vapours are mort copiouliy raifed ; fo 

 that though the air, properly fo called, be expanded and 

 confequently becomes hghter, yet its interl^ices being 

 croudcd with vapours and other matter fpeclflcally heavier, 

 the weight of the compound may continue m.uch the fame. 

 He alleges an experiment of Mr. C=ifwcll upon the fummit 

 of Snowdon hill to prove, that the tirll inches of mercury 

 have their portions of air fufficiently near to what he has de- 

 termined ; for ths height of the hill being nearly 1240 

 yards, Cafwdl found the mercury to have fubfided to 25.6 

 inches, or 4 inches below the mean altitude of it at the 

 level of the fea, and by his own calcularion the fpace anf- 

 wering to 4 inches fhould be 1288 yard?. 



M. De Luc has given an hiflorical and critical detail, in 

 his " Reche.-ches," vol. i. p. 159, &c. of the attempts that 

 have been made, and of the rules that have been propofed, 

 by Maraldi, Scheuchzer, I. Caffmi, D. Bernouiili, Horre- 

 bow, and Bouguer, asvvell as thofe of Pafcal, Perrier, Ma- 

 riotte, and Halley, for applying the motion of the mercury 

 in the barometer to the mcafurement of altitudes. But the 

 fubjetl has been further purfued, and with a peculiar degree 

 ef accuracy, by De Lac himttlf, fir Geo. Shuckburgh, 

 and Gen. Roy, as we (liall (hew in the fequel of this article. 



From the experiments of Boyle, Mariotte, Amontons, 

 and othera, it was inferred that the elalliclty of the air 

 is very nearly proportional to its denfity ; and this principle, 

 denominated the " Boylean law," was affumed by almoll; all 

 writers on this fubjeil. Thefe experiments, however, were 

 not very nice ; nor were they extended to any great degrees 

 of compreffion, as tVie denfity of the air was not quadrupled 

 in any of them. By the later and more accurate experi- 

 ments of Sulzer (Mem. BerUn. vol. ix.), Fontana (Opufc. 

 Phyfico-Math.), M. De Luc, fir George Sluickburg, and 

 Gen. Roy, it has been found that the elafticity of the air does 

 not incrcafe quite fo fa!l as its denfity. Fronri' the Beriin 

 txgeriments it appears, that the elatUcity of the air of the 



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temperature 55°, or the comprefling force, increafes f* 

 much more flowly than the denfity, that if the comprefling 

 force be doubled, the denfity will exceed the double by 

 about a tenth part, &c. The law of this variation is ex- 

 preffcd with tolerable exaiftnefs, by fuppofing that if D be 

 the deniity of the air, and F the force compreffing it, then 

 D = F ' ^", n being a very fmall fraftion, nearly .0015. 

 But new experiments are wanting to afcertain the law of 

 this inequality with precifion. Neverthelefs, the general re- 

 fult has been, that the elafticity of rarefied air is verj' nearly 

 proportional to its denfity ; and the Boylean law may in 

 general be affumed in caies of the greateft prattical im- 

 poi-tance, or when the denfity does not much exceed or fall 

 (hort of that of ordinary air. See Elasticity of tht 

 Air. 



If we fuppofe the air to be of the temperature of 32° of 

 Fahrenheit, and the mercury to ftand in the barometer at 

 30 inches, we muft allow -rath of an inch for its defcent if it 

 be elevated 87 feet; and, accordingly, if the air were equally 

 denfe and heavy every where, the height of the atmofphere 

 would be 30 X 10 X 87 feet, or about 5 miles. But as 

 the air is an elaftic fluid, whofe denfity is always propor- 

 tional to the comprefling force, the altitude of the atmo- 

 fphere will be much greater ; and the method of eftimating 

 it by Dr. Halley and others, admits of a familiar illuflration. 

 Suppofe then that a prifmatic or cylindric column of air, 

 reaching to the top of the atmofphere, were dirided into an 

 indefinite number of layers or ftrata of very fm.all but equal 

 thickncfo, and that every one of the particles of air that 

 form thefe ftrata were of the fame weight at all diftances 

 from the furface of the earth ; it is plain, that the quantity 

 of air in each ftratum is as the denfity of the ftratum, 

 or as the comprefling force, that is, the weight or quantity of 

 matter of the fuperior and incumbent ftrata; confequently the 

 quantity of air in each ftratum is proportional to the fuper- 

 incumbent air ; but the quantity in each Ifratum is the dif- 

 ference between the column on its bottom and on its top, 

 and, therefore, thefe differences are proportional to the 

 quantities of which they are the differences. But in.a fe- 

 ries of quantities proportional to their differences, the quan- 

 tities themfelves and their differences will be in continued 

 geometrical progreffion : e. g. let a, I, c be three fueh quan- 

 tities ; then b : c :: a — I rb — c ; and, by alternation, 

 b : a — b ■.: c : b — • c % and, by compofition, i> : a :: c x I, 

 and a : b :: b -.c. Hence it appears that the denfities of 

 the ftrata decrcafe in a geometrical progreffion ; that is, 

 when the elevations above the centre or furface of the earth 

 increafe, or their depths under the top of the atmofphere de- 

 creafe, in an arithmetical progreffion, the denfities decreafe 

 in a geometrical progreffion. This principle may be ap- 

 plied to the purpofe of meafuring atinofpherical altitudes in 

 the manner of Dr. Halley above ftated, or by means of that 

 fpecies of logarithmic curve, called from this application and 

 ufe of it the " atmolpherical logarithmic." (See Logarith- 

 mic Curve, and Atmofpher'tcal Logarithmic.) ■ Let 

 AR^ (fg. 99.) reprefent the feAion of the earth by a 

 plane pafling through its centre O, and let m OAAI be a 

 vertical line, and AE, perpendicular to OA, will be an hori- 

 zontal line paffing through A, a point on the lurface of the 

 earth. Let AE reprefent the denfity of the air at ./■/ and 

 let DH, parallel to AE, be taken in proportion to AE, as 

 the denfity at D is to the denfity at A ; and hence- it is evi- 

 dent, that if a logiftic or logarithmic curve EHN be drawn, 

 having AN for its axis, and paffing through the points E 

 and H, the denfity of the air at any other point C, in this 

 vertical line, will be reprefented by CG, the ordinate to the 

 curve in that point ; becaufe it is the property of this curve, 

 that if portions AB, AC, AD, of its axis be taken in arith- 



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