HEIGHT IN THK ATMOSPHERE AT DIFFERENT SEASONS IN THE YEAR. 493* 



In the annual curve, on the other hand, the epochs at the colder station are 

 retarded, 0' falls to the right of 0, and C is negative. Tan x, becomes positive, 

 and x^ recedes from 90° towards 0° ; hence the maximum difference precedes the 

 greatest annual heat. The greatest recession of x, from 90° is determined by the 

 limiting value 



tan X,— ^ — — 



and when C'=-180°, x^ of course becomes again = 90°. 



In the case of elevation in the atmosphere, the value of C, or the change of 

 epoch, is probably never extremely great, and the preceding investigation proves 

 the direction of its influence on the period of maximum decrement of temperature, 

 which experience confirms. But three terms would be required to be included in 

 the expression to obtain the result with accuracy, and the successive constants 

 may be derived from expressions similar to those for b and c. 



It is interesting to observe the circumstances which modify the precession of 

 the epoch of maximum difference in consequence of the retardation of tempera- 

 ture epochs at the colder station (as illustrated in the figure on the last page), 

 and vice versa. The comparative velocity of displacement of the relative maxi- 

 mum and absolute maximum will be furnished by the value of the differential 



coefficient ^ . 



Differentiating Eq. (6), 



dz, BB'cosC'-B'g 



dC 



and smce cos^ ..= TTun^" B'^-2B-BcosC + B^ '^ ^l' ^'^ 



dx, BB'cosC'-B'2 



dQ B'2-2B'BcosC' + B» 



When C = 0, or small, 



dx, BB'-B'2 B' ^ , , ,_, 



TG^ (B-B'y ^B^^ ' accurately or nearly (7) 



which is always positive, since B' ^^ B. 



Now the value of this quantity depends entirely on the ratio of B to B', or 

 the approximate ranges at the two stations. As B and B' are more dispropor- 

 tioned, the velocity of the motion of x^ diminishes ; and as they approximate, it 

 increases indefinitely. 



So far as the imperfect data of observation go, this taUies well with facts. 

 Thus, for the annual curves at Colinton and BonaUy, discussed in the preceding 



