XOTE ON A DIAGExVM SHOWIXG THE AMOFXT 

 OF AVAILABLE SUNSHI^'E FALLING ON A 

 HORIZONTAL SURFACE ON ANY DAY OF THE 

 YEAR AT A GIVEN PLACE, AND SHOWING 

 ALSO THE SUN'S ELEVATION AND ITS TIMES 

 OF RISING AND SETTING. 



By J. T. Morrison, M.A., B.Sc, F.R.S.E., 



I'lofe.ssor of Ajiph'ed MathenmticH, Universit n of SteUcnhogclt. 



MitJi Three Te.vt Figures. 



Read Jidij 15, 1920. 



1. The dia<^ram described in this note was found service- 

 able to students attending a short course on meteorology 

 given in 1919 in the University of Stellenbosch. It is probably 

 not new, but has not been met with in any of the text-books 

 or journals available to the writer. It can be constructed 

 easily in schools as an exercise on sines and cosines, and 

 may be helpful in supplementing the open-air observations, 

 which should be a part of all school courses on geography. 



2. If the intensity of the sun's radiation be regarded as 

 constant, the amount which falls j^er miniite on a horizontal 

 surface at the upper limit of the atmosphere at any given 

 place is, of course, proportional to the sine of the angular 

 elevation of the sun above the horizon. This amount may 

 be regarded as measuring the intensity of available sunshine 

 at that place. The construction given below provides an 

 easy graphical method of detennining the sine of the sun's 

 elevation at any hour of any day, and hence of calculating 

 the available sunshine. 



3. If we apply the well-known formula of spherical 

 trigonometry' 



cos a = cos h cos ^'+sin h sin c cos A 

 to the spherical triangle whose apices are P, the south pole 

 of the heavens, Z, the zenith, and >S', the sun, we have (see 

 Fig. 1) 



cos ZS = cos ZP cos 7^>S'+sin ZP sin P;S' cos P 

 Here S may be taken to represent either the true sun or the 

 " mean sun." As the latter proceeds uniformly along the 

 ecliptic, and as its hour-angle P changes in strict keeping witli 

 an ordinary clock, it is convenient to apply the formula to 

 the " mean suir " and draw our sunshine diagram for tlie 

 latter, leaving to a later stage tlie small corrections for the 

 difference between the positions of the true and " mean " 



