BAR 



BAR 



14000, and fiippofing tlie atmofphcrc to be equally deiife, 

 elilmatcd ils liciglit to be twice as great as Kepler's meafure, 

 or at lead 55000 feet. But when the elallicity of the air 

 ■was found to be in an inverfe ratio of the fpace which it 

 occupied, or that its coiidenfation was proportional to the 

 weight that comprcficd it, and of courfe that its dilatations 

 were in the inverfe proportion of the comprefTuig weights, a 

 property firft difeovered by Mr. R-chard Townley, and de- 

 monllratcd by Mr. Boyle, the height of the atmofphcrc was 

 more accurately afcertaincd. f.ir. Boyle's experiments to 

 this purpofe were publill'.ed in 1661, in his " Defenfio Doc- 

 trim de Aeris Elatere contra Liuum," and exhibited the 

 preceding year before the Royal Society. The law of the 

 dilatation of the air was difeovered alfo by M. Mariotte ; 

 and he pubiiflicd an account of his experiments for afcer- 

 tainiiig it. in 1676, in his " EfTai fur la Nature dc I'Air," 

 and " Traitc des Mouvemens dcs Eaux." This law was 

 generally admitted by philofophers, and it was confirmed by 

 obftrvation in all climates and at all altitudes. To this pur- 

 pofe, M. BougucT (Mem. Acad. Roy. Sc. 1753.) gives us 

 the refult of the experiments made by himfelf and M. de la 

 Condamine in America ; and he fays that he found, without 

 any exception, that tlie elafticities of the fame mafs of air 

 exaftly correfponded to the ratio of the denfities. M. Ma- 

 riotte applied this general law to the invelligation of the 

 total htight of the atmofphere. With this view, he coUefttd 

 many obfei-vations of the bai-ometer made at fmall heights ; 

 and he was the firll perfon who fuggefted the ulc of loga- 

 rithms in edimating heights by the defeent of the mercury 

 in the barometer, though this method has been generally af- 

 cribed to Dr. Haliey; and Hallcy indeed firll employed tables 

 of logarithms in the calculation of atmofpherical altitudes. 

 See Phil. Tranf. N^ 181, or Abridg. vol. ii. p. 14. Dr. 

 Haliey, affuming the fpeclfic gravity of the air to water, 

 when the barometer ilood at 30 inches, and in a mean Hate 

 of heat and cold, to be as 1 to 8co, and that of mercury 

 to water as 13-v to i, (fo that the weight of mercury to air 

 is as io8co to l, or a cylinder of air of I0800 inches or 

 900 feet is equal to an inch of mercury,) inferred from thefe 

 premifes, tliat if the air were of equal denfity, like water, 

 the whole atmofphere would be no more than 5.1 miles 

 high ; and that. for an afcent of every 500 feet, the baro- 

 meter would iink an inch. But the expanfion of the air in- 

 creafing in the fame proportion as the incumbent weight of 

 the atmofphere decrcafes, the upper parts of the air are 

 much more rarefied than the lower, and each fpace corre- 

 fponding to an inch of quickfilver is gradually enlarged, and 

 therefore the atmofphere muR be extended to a much 

 greater height. As thefe expanfions of the air are recipro- 

 cally as the heights of the mercury, they may be reprefented 

 for any given mercurial height by means of the hyperbola and 

 its afymptotes. Thus, in PLiteXl. Pnctimcilics,Jig. 98, the rec- 

 tanglcs[ABCE, AKGE. ALDE, &c. are always equal; and 

 confequently the fides CB, KG, LD, I'cc. are reciprocally 

 as the fides AB, AK, AL, &c. (See Hyperbola.) If 

 then AB, AK, AL, &c. be fuppofed equal to the heights 

 of the mercury, or the corrcfpondjng pred'ures of the atmof- 

 phere, the liues CB, KG, LD, &c. anfwering to them, 

 will be as the expanfions of the air under thofe preffures, or 

 the bulks which tlie fame quantity of air will occupy ; and 

 if thefe expanfions be taken infinitely numerous and infi- 

 nitely fmall, their refpeftive funis will give the fpaces of 

 air between the feveral heights of the barometer : i. e. the 

 fum of all the lines between CB and KG, or the area 

 CBKG, will be proportional to the diftance or interval in- 

 tercepted between the levels of two places in the air, where 

 the mercury would (land at the heights reprefented by the 

 lines AB, AK ; and, therefore, the fpaces of the air anfwtr- 



iiig to equal parts of mercury in the barcmeter are as t?i« 

 areas CBKG, GKLD, DLMF, &c. ; but thefe areas are 

 proportional to the logarithms ot the numbers e/.prefring the 

 ratios of AK to AB, of AL to AK, of AM to AL, &c. 

 Thus, by th« common table of logarithms, the height of 

 any place in the atmofphere, having any afilgned height of 

 the mercury, may very eafily be found ; for the hue CB in 

 the hyperbola, the areas of which rcprefent the tabular 

 logarithms, being 0.0144.765, we (hall have the following 

 proportion : as 0.OI44765 is to the diiicrence of the loga- 

 rithms of 30 and of any Iclfer number, fo is the fpace anf- 

 wering to an inch of mercury, if the air wereequa'ly prciTtd 

 with 30 inches of mercuiT, and every where alike, or yoo 

 feet, to the height of the barometer in the air, where it will 

 flaiid at that lefier number of inches. By the converfe of 

 this propofition, the height of the mercury may be found 

 conefponding to the given altitude of the place. It {hould 

 be obferved, that the number 0.0144765 is the mean be- 

 tween 0.0147232, the difierence of the logarithms of 30 

 and 29; and 0.0142404, the difference of the logarithms 

 of 30 and 31. The firit difference reprefents the mean 

 denfity of the air between the heights of 30 and 29 inche» 

 indicated by the barometer ; and the fecond diifereiice re- 

 prefents the Vnean denfity between 30 and 3 i ; and the den- 

 fity of the air at 30 inches is the mean between thefe two 

 denfities. This calculation of Dr. Haliey is founded 00 

 the fuppofition of equal and uniform gravity ; but fir Ifaac 

 Newton refolved the problem more generally (Princ. Phi- 

 lof. Nat. Math. 1. ii. ;j 5.), and extended it to the true 

 ftate of the cafe, where gravity is as the fquarc of the 

 dillance inverfcly ; ai.d he fiiewed, that when the diftances 

 from the earth's centre are in harmonic progreffion, the 

 denfities are in geometric progreffion. He alfo Ihews, in 

 gener.->l, what progrcflion of the diftances, on any fuppofi- 

 tion of gravity, will produce a geometrical progrellion of 

 the denfities fo as to obtain a feries of lines which will b« 

 logarithms of the denfities. See alfo Cotes's " Hydroftati- 

 cal Le£lures," and '.' Harmonia Menfurarum," and the ar- 

 ticle Hc}ght of the AxMOSPHtRE, and Atmofpherical LoG.'i- 

 RiTHMic in this diftionary. By thefe rules Dr. Haliey caW 

 culated the following tables : 



Given Hcigiits of 

 ihcMeicury, 



Inches 



30 



29 



28 



2-] 



26 



25 



20 



10 



5 



1 



0.5 - 

 0.25- 

 o.i - 

 0.0 1 - 

 0.00 1 



Altitudes. 



Miles 



Feet 

 — — O 



Given Altitudes. 



I Heightsof tlie 

 Meicuiy. 



915 



1862 



2844 



3863 



4922 



- 10947 



18715 



• 29662 



4«37«' 



91831 



110547 



129262 



29 or 154000 

 41 or 2 16169 

 53 o'- 278338 



Feet. 



o 



1000 — 



2000 — 



3000 — 



4000 — 



5:00 — 



Miles I - 



2 - 



3- 



4- 



5- 



10 ■ 



«5- 



ZQ- 



3Q- 



40- 



Inches 



30.00 



28.91 



27.86 



26.85 



25.87 



24-93 



24.67 



20.29 



16.68 



13.72 



11.28 



4.24 



1.60 



0.95 



0.23 



0.08 



0.012 



Upon thefe ftippofitions it appears, that at the hc'ght of 

 41 miles, the air is fo rarefied as to take up 3000 tinies the 

 fpace it occupies here j and at 53 miles high it would be 



, expanded 



