87 



The seconds in the latter part of the expression = 

 (;„— 1 ) tan. 9 ^ rp^ compute this quantity it is necessary ta 



a COS. * 9 stti. I *■ A ^ ,1 



know 7/?, / and a but not with much precision. 



If we take & = 80' and use, for the present, round numbers, 



^ I • 1 r>r\f\c> „J ^ Smiles I (m — I) Itan.Q ■, .,, 



lakmff w = 1,0003 and— = -rr— = -— -, i rr-^—r, = 14 



o ' a 4000 800 a cos. • d sm. \" 



nearly. The terms which have been neglected, must obvi- 

 ously be much less. The limit may be thus computed. 



Let the equations (S) and (5) of the last article be ex- 

 panded, neglecting products of three dimensions of s, f and 

 (^) and we shall obtain 



(0-f)) 



Now of the terms that compose the factor of ^ ''''"' , the 



'^ 2 COS. » r 



first 5 has already been considered and found not to produce 

 in integrating a quantity greater than a few seconds, as far as 

 ^=80° ; therefore after integration, the 2d and 4th on account 

 of the smallness of b (§) and b § must be quite insensible; but 



the third— i^ s ' tan. ' 6, will produce a term f _ ^f^"'^""''? =« 



S fbs^ tan. ^6 ^ 3 p 6 s'stan. ^ g . 



T7os7^ if 2co:i. » e 



The law of decrease of the density of the atmosphere is 



between that which a uniform temperature gives, and that of 



the density decreasing uniformly, as will be shewn further 



■on. The true value of the above integral, wiU therefore he 



