ATM 



As 9600 : 14 



Mean 49 1 

 Stand. 31 



DifF. i8i 



As 43 



29.388 



, . f 72o.?go fathoms 

 The altitude fought .s |^,. ^'^^z.y/^ kx-t. 



Example II. To find the altitude of a hill, when the 

 Hate of the barometer and thermometer, obfcrved at the 

 bottom and top of it, is as follows : viz. 



Tliermometers 

 detached 



35 

 3' 



Mean 33 



attached 

 38 



Ditr. 



3 



Barometers 



29.45 

 26.82 



As 9600 



Mean 3 3 

 Stand. 31 



DifF. 



: : 29.45 

 .01 



M = 29.44 

 jrt =. 26.82 



As 435 : 



.01 



logs. ' 



4689373 

 4284588 



404.790 

 1.86 



1.86 



r^, , • , r 1 . • ? 406.65 fathoms. 

 The altitude fought is | ^,. ^J^y_^> f^.^^_ 



~M.De Luc found that the height of the atmofphere, 

 fuppofing its limits where the mercury would ftaiid only at 

 one line, and the thermometer indicating o in his fcale, 17° 

 in that of Reaumur, and about 70° in Fahrenheit's, is 

 25105.45 toifes, or 11 leagues and 3 toifcs ; and in the 

 fame circumftances, if the mercury in the barometer funk 

 to -5,^ of a line, the height of that part of the atmofphere 

 would be 35105.45 toifes. 



Upon the principles above Hated, the following table is 

 calculated ; fuppofing firll as a mean of the obfervations at 

 the Puy de Domme in France, and thofe on Snowdon-hiU 

 in Wales, that at the altitude of feven miles, the air is 

 four times rarer than at the furface of the earth. 



A T M 



It might eafily be (hewn by purfuinpf the calculation in 

 this table, that a cubic inch o( the air we breathe would be 

 fo much rarefied at the altitude of 500 miles, that it would 

 fill a fphere equal in diameter to the orbit of Saturn. 



Hence it appears that the atmofphere, however indefi- 

 nitely it may be expanded, becomes at a comparatively 

 fmall diftance, fo rare and light, as to be utterly impercep- 

 tible in its effects as a refilling- medium : and if the atmo- 

 fpheres of the planets refemble that of the earth, theymuft 

 be fo attenuated at the diilances of the planets from one 

 another, as to give no fcnfible refiilance to their motions 

 round the fun for many ages. 



M. de la Hire, after Kepler, recurred to the more an- 

 cient method of afcertaining the height of the atmofphere, 

 viz. from the confidcration of the crtpufcula. It appears, 

 from the obfervations of aftronomers, of the duration of 

 twilight, and of the magnitude of the terreftrial fliadow in 

 lunar eclipfes, that the efieft of the atmofphere to reflcdt 

 and intercept the light of the fun, is fenfible to the alti- 

 tude of between 40 and 50 miles. So far then we may 

 be certain that the atmofphere reaches ; and at that alti- 

 tude we may colleif, from what has been already faid, 

 that the air is above 10,000 times rarer than at the fur- 

 face of the eatth. How much farther the atmofphere may 

 extend, we are altogether ignorant. Cotes's Hydrofc. 

 Left. p. 123. and 125. 



It is allowed by albonomers, that when the centre of the 

 fun is 18°, or allowing for the rtfraftion 17° 27', below the 

 horizon, the twilight begins or ends : now the ray which 

 we fee can be no other than a horizontal line, or a tan- 

 gent to the earth in the place where the obfervcr is ; but 

 this ray cannot come directly from the fun, which is under 

 the horizon ; and mull therefore be a ray reflefted to us by 

 the lad inner and concave furface of the atmofphere. \Vc 

 are to fuppofe that the fun when 17° 27' below the horizon, 

 emits a ray which is a tangent to the earth, and ftrikes 

 upon this lall furface of the atmofphere, and is thence re- 

 Hefted to our eye, being dill a tangent, and horizontal. If 

 there were no atmofphere, there would be no crepufcuhim ; 

 and confequently, if the atmofphere were not fo high as it 

 is, the crcpufculum would begin and end when the fun is 

 at a Icfs dillance from the horizon than 17" 27', and con- 

 trarily. — Hence we infer, that the extent of the arc by 

 which the fun is deprciTed when the crepufculum begins or 

 ends, determines the height of the atmofphere. We are 

 to note, however, that 33' muft be fubtrafttd from the 

 arc of 18" for the refradlion which raifes the fun fo much 

 higher than he would be ; and 16' more for the height of 

 the upper limb of the fun, which is fuppofed to fend the ray 

 above his centre, fo that the arc which determines the height 

 of the atmofphere is only 17° 1 1'. Two rays, one direA and 

 the other reflected, but both tangents to the earth, mult ne- 

 ceffarily meet in the atmofphere at the point of reflection, 

 and comprehend an arc between them of 17° 1 1', of which 

 they are tangents. — Hence it follows, from the nature of 

 the circle, that a line drawn from the centre of the earth, 

 and cutting the arc in two, will go to the point of con- 

 currence of thofe two rays ; and as it is eafy to find the ex- 

 cefs of this line above the femi-diameter of the earth, which 

 is known, it is eafy to find the height of the atm.ofphere, 

 which is only that excefs. See Cr.epusculum. 



On this principle, M. de la Hire difcovered the height of 

 the atmolpiiere to be 37223 fathoms, or near 17 French 

 leagues. The fame method was alfo made ufe of by Kep- 

 ler, who only rejected it, bccaufc it gave the height of 

 the atmofphere twenty times greater than he otherwife al- 

 lowed 



