ATM 



demondrated, in a very familiar and intelligible manner, 

 that if any number ofdillances fromtlie furface of the earth 

 be taken in an arithmetical progrtflion, the denl'ities of the 

 air at 'thofe diftances will be in a geometrical progrc'Tion. 

 Let xaax (Plate IX. PtirMnallcs, fg. 72.) reprefent a vcflel 

 reaching from the forface of the earth ax to the top of the 

 atmofphcre xx ; and let the fide ax be divided into inches 

 ch, he, cd, &c. and let the lines U; cl, dm, &c. be drawn 

 parallel to a^n. It is evident that the air contained between 

 ihefe parallel lines becomes rarer as v/e afcend, becanfe every 

 afcending parallel fuccclTively is pi-elfcd by a Itfs colnmn of 

 fupcrincnmbent air than the next below it. Suppofe then 

 that the air al is every where uniform, but dcnfer than the 

 air II, and fo upwards. Let the air U be reduced into a 

 lefs fpacs hq, fo as to become of equal denlity with the 

 air ak, bv making the fpace hq lefs than /■/, in the propor- 

 tion that the air hi is lefs denfe than the air ah. And let a 

 fr.nilar conftrudion be continued, fo as to reduce every 

 inch breadth of air to the fame denlity with the air al;. The 

 fpaces ah, hq, cr, &c. will evidently be as the denlities of 

 the feveral inches of air, ak, hi, cm, &c. and the qnautity 

 or weight of the fuperincumbcnt air belonging to each of 

 thcfe fpaces, and reaching to the top of the atmofphere, 

 will ahvavs be as the fum of aU the fpaces fituatcd above 

 any fpace propofed ; the quantity or weight being, hy the 

 conftrnction of the figure, as the fpace which it pcdelies. 

 Since then the dfnfity of the air is as the force which com- 

 prefles it, and this force is the quantity of fuperincumbcnt 

 air, the denfities of the air between av. and hi:,. Li and il, 

 cl and dm, &c. are to each other as the quantities of air 

 above ax, hi, cl, &c. up to the extremity of the atmof- 

 phere. But thefe denfities, by what we have already 

 fliewn, are as the fpaces ah, Lq, cr, &c. and the quni^ti- 

 ties of fuperincumbcnt air are as the fpaces xl0qrstvx, 

 xc)rslvx, xdhlvx, &c. ; therefore the fpaces ah, hq, cr, 

 &c. are to each other refpectively as the fpaces xh^qrstvx, 

 xcyrstvx, xdhlvx, &c. Now the former fpaces ah, hq, cr, 

 being the differences of the latter, and mutually propor- 

 rional, are, by a v.ell known theorem in proportion, in a ge- 

 ometrical progreflion ; as the diftances al>, ac, ad, are in an 

 arithmetical progreffion. And thus the denfities of the 

 air belonging to every one of the inches, continued to the 

 extremity of the atmofphere, decreafe in the fame geome- 

 trical progreffion ; and every the leaft variation of altitude 

 will caufe the fame proportionable variation of denfity in 

 the air. As the rarity of the air is reciprocally as its 

 denfity, we may conclude that if the diftances from the 

 earth increafe in an arithm.ttical progreffion, the different de- 

 grees of rarity of the air increafe in a geometrical progrcflicn. 

 Whence it is obvious, fince an arithmetical feries adapted to a 

 geometrical one, is analogous to the logarithms of the faid ge- 

 ometrical one, that the diftances are every where proportio.'al 

 to the logarithms of the correfponding rarities. It is alfo 

 plain, that, as the diftances or altitudes are proportional to 

 the logarithms of the denfities or weights of the air, any 

 height taken from the earth's furface, which is the differ- 

 ence of two altitudes to the top of the atmofphere, is pro- 

 portional to the difference of the logarithms of the two 

 denfities there, or to the logarithm of the ratio of thofe 

 denfities, and their correfponding compreffmg forces, as 

 meafured by the two heights of the barometer there. 



This law was firft obferved and demonftrated by Dr. 

 Halley, from the nature of the hyperbola ; and afterwards 

 by Dr. Gregory, by means of the logarithmic line. See 

 Phil.Tranf. N° i8i. or Abr. ibid, vol.u. p. 13. and Greg. 

 Aftron. lib. v. prop. 3. See the further illuftration and proof 

 «f it undet the article Atmofpherkal Logarithmic, 



6 



ATM 



From this propofition, having made two or three baro- 

 metrical cbfcrvations of the rarity or denfity of the air at two 

 or three different known heights, it is tafy to deduce a ge- 

 neral rule for determining its rarity or denfity at any other 

 height, or the height correfponding to any rarity or den- 

 fity ; and confequcntly the altitude of the whole atmofphere, 

 fuppofing the utmoft degree of rarity known, beyond 

 which the air cannot go. 



But it is to be obferved, that thefe computations of the 

 rarity of the atmofphere, at different heights, are four^ded 

 on this principle, that the denfity of the air is every where 

 proportionable to the fnperincumbent weight. And this 

 rule holds true only upon the fuppofition that the heat is 

 uniform at different diilances from the cajth ; for if the 

 ftir be hotter in one part than in another, the air will be 

 more rarti'ed in the hotter part than it will be in the cooler, 

 although preffed by the fame weight, or at the fame alti- 

 tude above the earth's fnrface. 



It muft not be here o:nitted, that fome obfervations made 

 by Caffmi, and his nffociates, feem to render this method 



precariou.< In continuing the meridia:; line of the obferva- 



tory at Paris, they meafured the altitudes of fe-eral moun- 

 tains with great accuracy ; noting the height of the baro- 

 meter at the top of each ; and found, that the rarefactions 

 of the air, as you afcend from the level of theesrth, are much 

 greater than they ought to be, accordmg to this proportion. 

 Snfpefting therefore the juftneis oi tlie experiments, the 

 Royal Academy made divers others, under great dilatations 

 of air, far exceeding the rarities found on the tops of the 

 mountains; the rtfult whereof was, that they all exactly an- 

 fwered the proportion of the incumbent weights. Whence it 

 fhould follow, that the higher air about the tops of moun- 

 tains is of a different nature, and oblervcs a different law 

 from that near the earth. 



This may be owing to the great quantity of grofs vapours 

 and exhalations here, more than there ; which \apours being 

 lefs elaftic, and not capable of fo much rarefadlion as the 

 pure air above, the rarefactions of the pure air increafe in a 

 greater ratio than the weights diminiih. M. FontcncUe, 

 however, from fome cxperim.ents made by M. de la Hire, 

 accounts for the phasnomenon in a different manner ; al- 

 leging, that the elaftic power of air is incrcafed by the ad- 

 mixture of humidity therewith ; and confequcntly that the 

 air near the tops of mountains, being moifter than tha't be- 

 low, becomes thereby more elaftic, and rarefi'-s in a greater 



ratio than naturally and in a drier ftate it would But Dr. 



Jurin Ihews, that the experim.ents produced to fuppcrt this 

 fyftem are by no means conclufive. Append, au Varenii 

 Geograph. 



M. Bouguer likewife, in the Memoirs of the Royal Aca- 

 demy of Sciences at Paris for the year 1 75 3, intim.ated his 

 opinion, that the condeiifations of the atm.ofpheic did not 

 obfervc the fame law at different heights : and endeavoured 

 to account for the variation, bv fuppofing that particles of 

 air at different heights are poffeffed of unequal detrrees of 

 elafticity. If this were the cafe it would be impoffible to 

 apply the barometer to the rretifuration of heights with any 

 degree of certainty. But M. de Luc has fhewn, by his 

 more accurate experiments, that this pretended inequality 

 of fpring in the particles of air does not fubtift ; and that 

 its condeiifations and dilatation^ follov; the fame law uni- 

 formly at all heights and in all clim.ates, excepting only the 

 differences that are caufed by heat, and other local circum- 

 ftances. Admitting therefore tlie principle above ftated, as 

 applicable to all altitudes within our reach, or as far as the 

 fummits of the higheft mountains on eartii, when a correc- 

 tion is made merely for the difference of heat or tempera- 

 ture, 



