INTENSITY OF SUN'S HEAT AND LIGHT. 



11 



This important law appears to have been first published in the Pyrometry of 

 Lambert. 



This point being established, let us, in the next place, compare the intensities 

 received by the Planets during entire revolutions in their orbits. In the preceding 

 formula, making 6 — 6' equal to an entire circumference, the sum of the intensities 



27t 



during a complete revolution, is found to be u = — — -.. Let this refer to 



° L A n >/ 1 — e 



the earth, and accenting the values for any other planet, u' = - . -Now 



A' n' V 1 — e 



n,ri, being inversely proportional to the planets' periodic times, we have by the third 



• 3 3 



law of Kepler, n 2 : n' 2 : : A' 3 : A 3 , or n A 2 = n' A 2 . Whence by substitution and 

 division, we obtain for the relative intensity upon any planet in an entire revolution, 



V A (1 — e-) 



(10). 



u VA'{l—e rl ) 



In like manner, the ratio of intensity for equal times, depending simply on the 

 inverse square of the distances, will be represented by 



u A'- 

 With these last two formulas, the following table has been prepared from the 

 usual astronomic elements : — 







The Sim's Relative Intensity 



upon the Principal Planets. 









IN EQUAL TIMES. 







In a whole 

























Mean Distance. 



Perihelion. 



Aphelion. 



Mercury .... 



1.643 



6.677 



10.573 



4.592 



Venus . 











1.176 



1.911 



1.937 



1.885 



Earth . 











1.000 



1.000 



1.034 



0.967 



Mars 











.813 



.431 



0.524 



0.360 



Jupiter . 











.439 



.037 



.041 



.034 



Saturn . 











.324 



.011 



. .012 



.010 



Uranus . 











.228 



.003 



.003 



.003 



Neptune 











.182 



.001 



.001 



.001 



It should be observed that the foregoing table does not take account of the 

 different dimensions of the planets, but refers to a unit of plane surface upon their 

 -disks, which is exposed perpendicularly to the rays of the perpetual sun. Upon 

 the disk of Mercury, the solar radiation appears to be nearly seven times greater 

 than on the Earth ; while upon Neptune, it is only as the one-thousandth part, in 

 equal times. In entire revolutions, however, the intensities received will be seen 

 to approach more nearly to equality. 



The intensities are thus unequal; and, by a calculation founded on the apparent 

 brightness of the planets as estimated by the eye, Prof. Gibbes has shown, in the 

 Proceedings of the American Association for the Advancement of Science for 1850, 

 that the reflective powers are also greater, according as the several planets are more 

 distant from the Sun. 



