On Atmospherical Refraction. 363 



/I ss]2r\ , rr (dm—dt Ap\ , ^ . ^ , , . 



I 7r\ — "'^— h-^h ••he coefficient of rfr beinar 



\w 2JssJ ssw[ m—t pj ^ 



equ^lto^:!L-,^ud(2p-I^^^^(p + ir)^,IL{^!li:3., 

 r -s \ s ) r \ sswj p ssw [m — f / 



— being 3.4.1, and m — t, on this supposition, 519. The pro- i 



-— — '^ ..»™...~... / 



the thermometer varies from 50° ; and — beina: also -At^, 



will be — — — — — = .003. The variation of t can only 



fii—t 519x500 ^ 



be determined from conjecture ; but supposing the alteration of 



temperature to cease at the height of about 4 miles, it must 



increase, with every degree that the thermometer rises at the 



earth's surface, about -^i-^, and — being ^i-^, will be 



t VI— t 



247 



= .004. The alterations of the barometer will affect 



519X120 



dp 

 p only, — being -^^ for every inch above or below 30. It is 



. . ^ . 3938 X 5280 x 12 , , . , , . , „ . 



evident, smce»j = , ^ __ , , , h bemg the height of the 



I0.57 hd 



barometer, and d the bulk of air compared to that of water, that 

 m must diminish, as well as p, when the temperature increases ; 

 and the correction for I being subtractive, the three variations will 

 co-operate in their effects ; but the proportion will be somewhat 

 different from that of the simple densities. If we preferred the ex- 

 pression derived from Professor Leslie's hypothesis, we should 



, , , . 2dw „ d^ , , 



merely have to substitute-- — - tor and the variation 



•' 1 -I- 2n m—t 



depending on the law of temperature would become about f as 



great. It must, however be limited to such changes as affect the 



lower regions of the atmosphere only, its " argument" being the 



deviation from the mean temperature of the latitude ; but even 



in this form it cannot be satisfactorily applied to the observations 



at present existing ; although it appears to be amply sufficient 



