3!&4r. Astronomical and Niiuticul Colleclioiis. 



dz 

 but AU — — f/i-e""" — vAz — — fji.ve—'"* — — Az: and ini- 



tially, when m = 0, i7" = f* — >, dz" = d.r, or if 1/ — /* 



1 — pU 



•r: >., dz = , C = w;? + — , dl/ = /itv — — vdz i:: 



1 + pA X X 



dx , "X J 1 d^" > oj- 1 "* 



- ^1, + ax, and — 1- z= I :=: 2^ + . 



1 + p;i 1 + px d.r XA 



1 + pX X\ 1 + P^ AA 1 + pX 



The numerical values of the coefficients, taking m = 798, as sup- 

 posed by Laplace, will be S= —2 — = — + = — + 



2mp 2 2j)X 2 1373.86 



=: 2.977, and C n= ^ (1 + i- ") == ^ (1 + I^ + '. 



3p wi / 3p VI 1 +pA 



y - 2fx. \ _ .9923 .^ _^ QQ^^ _j_ 1348 x 25.82 \ _ 



XA / P 1.2019x687x687/ 



3141 (1.0074 + .0614)=3141 x 1.0688 = 3356. In the Nautical 

 Ahnanac,\he values, obtained from the observed refractions only, 

 are B = 2.97 and C = 3600 : and the difference in the results 

 of the computation will be insignificant even at the horizon. 



It is almost unnecessary to remark, that a hypothesis, so well 

 supported by direct observation, can scarcely be very materially 

 erroneous. With respect to the variation of temperature in 

 ascending, we may represent it by making z = 3/(1 + f.r — f); 

 (CoZZec^ VI. i. 7. D.); t being either constant or variable, ac- 

 cording to the conditions of the hypothesis ; then if f be the 

 number of feet required for a depression of a degree of Fahren- 



, ., , „ , ^ _ 20 900 000 , . 43907 , , 



heit, we shall have t = , and / =r ; but 



476/ t 



z A-' 



dz = dy — + ty Ax + (.r — 1) yAt; consequently t n — ^ 



?/ yAx 



- ± ^ - (,r - 1)^, and dr = d f -^ - ^ h\ 



- yy Ax Ax \ yAx yy Ax J 



