LOCAL CLIMATOLOGY. 05 



altitude for the day (l)eing the correction for the absorption 

 of heat by the atmosphere) ; 

 is to 80^ Fahrenheit (the average for the year at the equator) : 

 so is the sine of the sun's altitude at noon for any day or latitude, 

 multiplied into the length of the day, and this product mul- 

 tiplied by the average altitude of the sun for the day ; 

 to the temperature for the day in degrees of Fahrenheit. 



Or, to put the formula into a briefer form : Let sin. A stand 

 for the sine of the altitude at noon, D for length of the day, and 

 C for correction for average of altitude at the equator ; then sin. A', 

 and D' and C, will stand for corresponding values for any day in 

 any other latitude ; and we have, with T for temperature. 

 As sin. A X D X C : 80°: : sin. A' X D X C : T. 

 If now we call D, in the first term of the first ratio, unity, and 

 make D' a fraction obtained by dividing the length of the day 

 between sunrise and sunset by 12, we shall simplify the operation 

 of computing for the values of T. 



By the use of this formula, I have computed the average tem- 

 perature, with that for the hottest and for the coldest season, for 

 each latitude in the northern hemisphere.* 



* The results given in this Table differ somewhat from those that have 

 been previously given, especially in giving a lower temperature for the 

 higher latitudes ; and as the importance that should be attached to the 

 results of any computation depend alike on its method and its data, I give, 

 for the satisfaction of those who may desire it, the brief outline of both. 



Let S and S' denote the sun at different alti- ? 



tudes, S being perpendicular. Then S' will 

 denote the sun at a declination from the zenith 

 equal to the angle SaS', which angle we will 

 call the zenith distance of the sun, or simply 

 Z. Now it is manifest that a ray of heat 

 coming from the sun at S, and dispersed over 

 one square foot, ab, will become dispersed over 

 a rectangle elongated to ac, when the sun has c 6 



declined to S"; and this elongation is equal to the secant of Z. Hence the 

 intensity of the light in the rectangle ac will be — ^ ; that on the square 

 ab being unity. But — = cos., and the cosine of any angle is equal to 



the sine of the complement ; but the complement of Z is the sun's alti- 

 tude, or angular distance from the horizon. 



Hence there can be no doubt that the sine of the sun's altitude =sin.A, 

 is an expression for the intensity of the sun's rays at any place or time, 

 after deducting what is absorbed, or perhaps the difference between what 



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