150 Prof. Bischoffo« the Temperature of 



conical mountain, whose sides make an angle of 30° with the ho- 

 rizon. The relations will be the same, if from B (PI. II. Fig. 9.) 

 there extend a large plateau. The increase of temperature to- 

 wards the interior of the earth will still advance more slowly 

 in a vertical direction from B than in plains. But at a certain 

 distance from B at K, the same increase of temperature will be 

 found as in plains. In order to find the point K, we will sup- 

 pose the temperature of the earth's crust at I to be if higher 

 than at B. If, further, the temperature at L be 1° higher than 

 at K or at B, we shall have 



IL = (1— y)« 



KL = n 



K N = m y 



but since 



I N = I L sill a = (1 — y)n&ina 

 L N = I li cos a = (1 — y)n cos a 

 K I> — L N = K N 



by substituting the values of ihese lines, we shall have 



;; — (1 — y) n COS a = m y 



from which we get 



«(1 C05«) 



m — n co.s a 



Substituting tiiis value of;//, we find 



ft'' ( I — cos a) in n — ii'- 



I L = yi 



- n cos a 



- -, (mn — M-'lsina 

 I N = -^ — ~ 



K N = 



m — 71 cos a 



m n (1 — cosn) 

 m — ?» cos (( 



If I B and N K be prolonged till ihey nieet in O, we shall have 



■NT r\ T XT . ('" '' — "■') sin a tariff ii 



N O = I N tang a = -i '- i2 — 



111 — 11 cos a 



OK=NO— KN 



_ (mn — 71-) sin a tang a — m n(\ — cos a) 

 m — It cos a 



B K = O K cotang a 



(m n — n^) sin a — >» n ( 1 — cos a) cotang a 

 m — n cos a 



