Vol.1] Hall. — Botanical Survey of San Jacinto Mountain. 35 



area but iueliued at dififerent angles to the direction of the rays. 

 For this purpose a trigonometrical formula may be developed to 

 give the ratio between the amount received by a surface inclined 

 at any given angle to the level and a level surface of equal area, 

 the sun's rays coming at any given angle. 



Since the amount of heat received by a surface is proportional 

 to its width we shall, for convenience, select a surface the width 

 of which is equal to the diameter of a ray of heat. Moreover we 

 shall consider only south slopes. 



In the diagram let 6 be a surface, as indicated above, inclined 

 at any given angle, £, to the level; let c be the level surface on 

 which the rays would strike if not intercepted by h; ^ is any 

 given angle at which the rays strike the level. 



Now since the number of rays striking & is equal to the num- 

 ber that would strike c if not intercepted, we have 



Distance betw een rays on h ])_ 



Distance between rays on e c 



sin P 



sm y 



sin /3 



sin ( 180°— ^—/8), 



or, since the amount of heat received by a surface is inversely 

 proportional to the distance between the rays, we have 



Heat rec'd bv unit area on h sin (^ + /5) 



Heat rec'd by equal area on c 



sm 



/? 



