INTENSITY OE SUN'S HEAT AND LIGHT. 



13 



SECTION III. 

 LAW OF THE SUN'S INTENSITY AT ANT INSTANT DURING THE DAT. 



The rays which emanate from the Sun's disk into space proceed in diverging 

 lines in the same manner as if they issued directly from the centre. And, on 

 arriving at the Earth, their intensity as before stated will be inversely proportional 

 to the square of the distance. 



But the more obvious phenomena of solar heat and light are manifested to us 

 under a secondary law. The Sun's intensity first becomes sensible in the eastern 

 rays of morning ; it gradually increases to a maximum during the day ; it declines 

 on the approach of the shades of evening, and becomes discontinuous during the 

 night. On the morning following the same course is renewed, and continued suc- 

 cessively through the year. Ordinary sensation and experience lead us to associate 

 the degree of solar heat at any part of the day, with the apparent height which the 

 sun has then attained above the horizon. Indeed, theory determines that at four 

 in the afternoon, or any other instant during the day, the Sun's intensity is propor- 

 tional to the length of a perpendicular line dropped from the Sun to the plane of 

 the apparent horizon, or varies as the size of the sun's altitude. 



The reason of this secondary law will be understood by regarding the beam of 

 solar rays which traverses in a line from the sun to the observer, to be resolved, 

 according to the parallelogram of forces, into a horizontal and a vertical component. 

 The horizontal component running parallel to the earth's surface is regarded as 

 inoperative, while the vertical component measures the direct heating effect. 



This relation is more fully shown in the annexed figure, where A denotes the 

 sun's apparent altitude above the horizon. The sun's intensity or impulse in an 

 oblique direction will be measured by the inverse square of the distance, or the 

 direct square of the sun's apparent semi-diameter A. If, therefore, A 2 denotes the 

 intensity of the rays in a straight line from the 

 sun, A 2 sin A, will be the vertical component or 

 heating force of the rays. And these terms being 

 in ratio as 1 to sin A, the latter component will 

 be represented by a perpendicular line from the 

 sun's centre to the horizon. 



Instead of thus decomposing the intensity after 

 the manner of a force in Mechanics, as first pro- 

 posed by Halley, in 1 693, the same law may be obtained in an entirely different 

 way from the principle of the inverse square of the distance. The latter mode 

 appears to present it in a more evident light, and was suggested in the original 

 beginnings of the present investigation, which were published in Silliman's Journal 

 of Science for the year 1850. 



It proceeds as follows: — 



A s-in.A. 



