INTENSITY OP SUN'S HEAT AND LIGHT. 



eccentricity, and 6 the true anomaly estimated from the perihelion; then, by 



Analytical Geometry, p = — i— — — L ; and hence, 

 1 + e cos 



«•„»_ (R-r) ( l + ecosO) 



A\l-e>) ■ 



Here for special values, making cos 6 successively equal to — e, + 1, — 1, and 



cancelling factors, we obtain for the values of sin z in order: — 



Average, sin z = — 



(2.) 



Maximum, sin z = 



A 

 R- 



A(l 

 R- 



■«) 



(3.) 



Minimum, sin z _ 



A (1 + e) 



Again, taking the length of arc z in the circle whose radius is 1, the breadth of 

 the differential zone upon the planet will be rz ; but since, for all the planets, z is 

 less than 1°, its sine may be substituted from either of the former equations, and 

 the same value essentially is represented by 



Linear breadth of zone = r sin z. (4.) 



It is also proved in Geometry that the surface of a sphere whose radius is r, is 

 equal to 4r 2 7i; n denoting 3.141592; and that the surface of a spherical zone is 

 equal to its altitude multiplied by 2 r it. Now, the altitude of the zone of differ- 

 ential radiation is, in ratio to that of the whole planet, as sin z to 2, or i sin z to 1. 

 Hence, representing the whole area of the planet by 1. 



The proportion of irradiated surface = i + i sin z. (5.) 



Whole surface irradiated = (J + § sinz) 4 r 2 n. (6.) 



Surface of the zone = 2r 2 7t sinz. (7.) 



If r be taken in miles, the area will be given in square miles. 

 The following table exhibits some of the primary phases of solar intensity upon 

 the planets ; and was obtained by substituting the proper astronomic elements in 

 formulae (3), (4), and (5). 





Average breadth 



Greatest breadth 



Least breadth 



Proportion of 





of zone. 



of zone. 



of zone. 



surface irradiated. 





Miles. 



Miles. 



Miles. 





Mercury ..... 



17.89 



22.32 



14.96 



.505991 



Venus 













61.12 



61.54 



60.70 



.503190 



Earth 













18.29 



18.60 



17.98 



.500231 



Mars 













6.42 



7.07 



5.87 



.500152 



Vesta 













.26 



.28 



.24 



.500980 



Jupiter 













34.87 



36.62 



33.28 



.500404 



Saturn 













18.17 



19.25 



17.21 



.500222 



Uranus 













4.01 



4.20 



3.83 



.500117 



Neptune 













6.14 



6.19 



6.08 



.500087 



In obtaining these tabular results, the earth's mean distance from the sun was 

 taken at 95,273,870 miles, and its radius at 3,962 miles. 



It will be perceived that the vast magnitude of the sun brings advantages of 



