ON THE 



RELATIVE INTENSITY OF THE HEAT AND LIGHT OF THE SUN. 



SECTION I. 



ON THE PROPORTION OF A PLANET'S SURFACE WHICH IS IRRADIATED BY THE SUN 

 AT ANY GIVEN TIME. 



It is evident that the extreme rays proceeding from the sun to the planet are 

 tangent to the two spheres, as shown in the annexed diagram; where S denotes 

 the centre of the sun, and P 

 that of the planet. 



Let PS = p, the radius-vec- 

 tor, or distance of the planet's 

 centre from that of the sun. 



Let ST = R, the radius of 

 the sun, and PA = r, the ra- 

 dius of the planet, regarded as 

 a sphere. 



Through P, let a plane be 

 drawn perpendicular to PS, and dividing the planet's surface into tAvo equal hemi- 

 spheres. The sun, being the greater body, illuminates not only the adjacent hemi- 

 sphere of the planet, but also the zone or belt, AC, lying beyond; which may be 

 called the Zone of differential radiation. 



Let the angular breadth of this zone APH = z, and, drawing AN or p parallel 

 to PS, the angle TAN is obviously equal to APH or z, since the including sides 

 of the one angle are respectively perpendicular to those of the other, and, therefore, 

 have the same relative inclination. Then, in the triangle ATN, which is right 

 angled at T, by the condition of tangency, 



sin TAN = 



NT 



AN' 



or 67 n z = 



R 



(1-) 



That is, the sine of the angular breadth of the zone of differential radiation is 

 equal to the difference of the radii of the sun and planet divided by the radius-vector 

 of the planefs orbit. 



To express this value in another form, let A denote the semi-transverse axis of 

 the planet's orbit, or its mean distance from the sun; let e denote the ratio of 



