140 Astronomical and Nautical Collections, 



tzdz 2 z s 



V 3 'J o 



hP — d M» _L hi* _L 



1 r (l-z)'d: „ / -_4_ J^ ^_ "\ 



i/ o m* 1 * A 3 V2-3 " V 3a ' 



hi* _L 

 z 



A= .719064 V^- 



(l-z)'dz __ 642767^^ 



L X 



ul± 



z 

 Now the value of v — V( a " — s" — 2pxs), becomes here 



V (y — 1 - 2p x ) ; and since x — 1 = AU =s — / ?L , 



makin^yda- = s, or a; s = (~ + l) 5 , we have x" — 1 = S* + 2s; 

 but the actual extent of the atmosphere is so limited, that we 

 may neglect S 2 , in comparison with 2 H, without sensible error, 



and make a? — 1 = 2s, and dr = 



pd: _ — P dz 



V(2H-2 P% ) V2 VS 



S / V'2'V-2H 8 



g!x 8 . _5_ pV ■ ^ _ ^f_ f-ii- + _L^^ + .£ 

 S« lb s a *"' V2 V V* 2 I§ 8 



i—^ — - + . . . ). This expression is applicable to every hypo- 

 thesis by which the relation of x to z can be expressed ; and in 

 the case of a uniform temperature, since dy s= — rnzdx — dz, 



and dx = ~ 1, we have s = — / — — = — hi — , and 

 mz J mz m z 



j •»! ( dz .1 vdz .3, 2 

 dr si — p i / — ( + _ mp -± 4- — wi'p* 



1 v /hi_L z hi* _L 



V z z 



_^!il_ + A ^p s _i£^l_ + . . . ). Then, by the integration 

 hF i- 1& ' hi* L 



z 



