WITH HEIGHT AT DIFFERENT PERIODS OF THE DAY AND YEAR, 491* 



POSTSCRIPT.* 



I am glad to find that the reasoning I have employed in page 494, to account 

 for the diurnal variations of the decrement of heat in the atmosphere, is entirely 

 confirmed by the observations of Eschmann, Kaemtz, and Horner, in Switzerland, 

 recorded in Poggendorff's Annalen, xxvii. 345, and in Dove's Repertorium, iii. 

 331. By projecting these observations graphically, I have found that the course of 

 the diurnal curves is such as I have described it to be, the variations on the moun- 

 tains preceding those on the plain, which, by reasoning similar to that in p. 493, 

 will give a maximum difference in the afternoon, and a minimum in the morning. 

 Thus the diurnal summer curve gives the minimum temperature of the day on 

 the Rigi at ^^ 43" a. m., and at Zurich at 4'' 14" a. m. ; whilst the maximum at the 

 former station occurs at 12" 54", and at the latter at 2^ 28" p. m. Also, it appears 

 by projection, that the difference of temperature at the two stations increases from 

 4'' 31" A. M. until 4'' 51" p. m., when it attains its maximum, and then declines. 



It is well known that the curves of temperature, whether diurnal or annual, 

 may be expressed with any required degree of accuracy, by a series of terms of 



the form 



A + Bsm(;»; + C) + Dsin(2a; + E)&c. Eq. (1) 



where x is the time, expressed, (in the case of the diurnal curve), by the horary 

 angle. If, then, the diurnal curves at the two stations be represented by two 

 such series, the difference will universally be represented by a series of exactly 

 the same form. 



Thus, if the series written above express the ordinates of the curve (annual 

 or diurnal) at the lower or warmer station, and the following 



A' + B'sin(;i; + C') + D'sin(a: + EO &c. (2) 



that at the upper or colder (in which, generally. A' -^ A, and B' ^ B, because the 

 range is less, as well as the temperature lower, and because the second term pre- 

 dominates greatly over the succeeding ones), — then the difference of temperature 

 of the two stations may always be expressed by a series of the same form {x, 

 the time, being still the independent variable), namely, 



o + 6sin (a; + c)+ &c (3) 



where o=A-A'; 6=\/B'^ + 2J3B'cos(C-C') + B'2 (4) 



, , BsinC-B'sinC 

 and tanc=— — — /s\ 



BcosC-B'cosC ^^' 



and so of the others, 



* Added by permission of the Council, April 1840. 

 VOL. XIV. PART II. 4 L * 



