( 586 ) 



further is : 



/> \-\-at f a (/„ — t) s . 



p l+at \ l-f«* 



if we put = \r. 



When dividing equation (II) by (III), we get: 



*( L ) 



R p 1— #' 



P* 

 while by differentiating Logarithmically we find: 



-© 



+ 



p 1 — »> ^ 



From the two last equations follows: 



d V = 7 <^-(i-#)-M = •;./.•> + (1-0)7--. • (iv) 



A ( i] | it ( 1 — to) 



According to Ivory's theory #=ƒ«*, where ƒ is a constant value 



(Radau assumes 0,2); if we introduce this relation into the equation 

 (111) we obtain after integration : 



y = 0,4^ m — 1,8420081 - Br. log (1— to) . . . ( V) 



By substituting (V) in (1) we can therefore calculate for each 

 value of to the value of ds according to Ivory's theory. 



6. Now I proceed to determine the relation between to and y 

 according to the temperature table II. 



Of two horizontal planes, one above the other, the first is situated 



n kil. {n a whole number), the second n' kil. {n' = or <[ n + I) 



above the surface of the earth ; their distances from the centre of 



the earth are r n mid ?y , their temperatures t„ and t n > and the values 



of y, y u and y n > . The temperature between n and n' varies regularly 



with the height and, to simplify the formulae, I suppose t„ — t n > 



a (t n — t n ') 

 proportional to y H > — y», so that, if#„ = — : 



1 -\-at n 



R 



- iyw — y») = c n &» (VI) 



r„ 



R 

 Hence tollows — dy=c n d& and after substitution of du in (IV) 



