LOCAL CLIMATOLOGY. 67 



bered, there are no clays followed by nights of radiation and cool- 

 ing, just as in winter there are no intervals of snnsliine to interrupt 

 the process of cooling ; and it is probable that the prolonged 



the distance CM, and its path is denoted by the curve line EM'. But on 

 any day and in a high latitude, when the day is more than twelve hours, 

 the curve denoting the sun's path should start at some point outside of E, 

 as at E'; and on a day when the time between sunrise and sunset is less 

 than twelve hours, the line should start at some point inside of E", as E". 



Now it is manifest that the amount of heat in any solar day is equal to 

 the space contained between the base line ECW and the curve line above 

 it, whether it be EMW or E'M'W, &c. This curve line is very nearly, 

 if not quite an ellipse. I am inclined to think that the ordinates in all 

 cases, except when CM = EC and the curve is a circle, will be found for 

 the first part of the distance E'C too long for an ellipse, and in the latter 

 part a little too short, until, of course, we come to CM', which will be the 

 half minor axis of an ellipse, EC being the half of the major axis. Still, 

 however, the figure is nearly enough to an ellipse for all the purposes now 

 before us. 



Changing somewhat the ordinary notation for an ellipse, let us, for the 

 convenience of the notation, denote the half of the minor axis, which is, of 

 course, sin. A, by A, and the half of the major axis, which is half the time 

 between sunrise and sunset, by D, and we have the heat of the day denoted 



, AI>7t 



by-^. 



But A, in this formula, denotes the greatest altitude of the sun, or the 

 half of the minor axis of the ellipse. If we recur to the process of obtain- 

 ing the formula AJ)7t for the area of an ellipse, we have 



V 



and, by consequence. 



=f> 



Whence it appears that if we divide — - — by D, we get the average 



Li 



value of A ; that is, — ^=— represents a parallelogram wliose base is D, 



and whose altitude li equal to the quotient of this fraction, — ^— , divided 



Krr 



by D, or -^— , which is half the sine of the sun's altitude into 3.141, &c. 



Hence I use the average thus obtained as a correction for the absorp- 

 tion spoken of in the text : this correction, for the perpendicular rays of the 

 sun, is .6. Hence, by multiplying the sine of the sun's average altitude for 

 midday by .6, and by the length of the day, 12h. for the first term in the 

 proportion, and then multiplying the sine of the sun's altitude for any other 



