METEOROLOGY. 327 



of evening, and becomes discontinuous during the night. On the 

 morning following the same course is renewed, and continued succes- 

 sively 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 the sun' s intensity is proportional to the 

 length of a perpendicular line from the sun to the plane of the apparent 

 horizon; that is, it varies as the sine 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 in- 

 tensity or impulse in an oblique direction will be measured by the 

 inverse square of the distance, or -the direct square of the sun's appa- 

 rent serai-diameter A. If, therefore, A^ denotes the intensity of the 

 rays in a straight line from the 

 sun, A2 si7i A, ivill he 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 1693, 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.*^ "^ 



The intensity at a fixed distance being as the sine of the altitude, 



*Let L =z the " apparent" latitude of the place, 

 D^the sun's meridian declination, 

 Ai^the sun's apparent eemi-diameter, 

 ^rrthe sun's altitude, and 

 /i mthe hour-angle from noon. 

 The horizontal section of a cylindrical beam of rays from the sun's disk ujxin a plain oa 

 the earth's surface, is well known to be an ellipse ; and if 1 denote the suu's radius, 1 will 

 likewise denote the semi-conjugate axis of this projected ellipse; while the horizontal pro- 

 jection, -;: — — will be the semi-transverse axis. The area of the elliptic projection is, there 



fore, 1 X -. — 7- X rr. But the intensity of the same quantity of heat being inversely as the 



space over which it is diffused, the reciprocal of this area, or ain A, on rejecting the constant 

 TT, will express the sun's heating effect, supposing the distance to be constant for the same 

 day. But, on conipiiring one day with another, the intensiity further varies inversely as the 

 square of the distance, »hat is, directly as the square of the apparent diameter or semi-dia- 



