M. Arago on the Light of' Comets. 25 



the circular opening at the distances 1, 2, 3, ... , 100, will be 

 among themselves as 1, 4, 9, ... , 10,000. 



Thus, on the one hand, 4he intensities of the luminous open- 

 ing would augment as the number of the illuminating points, 

 or as the squares of the distances ; but, on the other hand, on 

 account of the divergence of the rays, the quantity of them 

 which the opening embraces diminishes for each illuminating 

 point proportionably to the same series of numbers. These 

 two effects, therefore, exactly compensate each other, and there- 

 fore also, at all distances the opening should appear equally 

 bright. 



A very simple example will fix, without any ambiguity, the 

 true meaning of this important result. 



The sun, seen from Uranus, appears to be a very small circle 

 of 100". Well, then, do you, an observer, standing upon the 

 earth, place between your eye and the sun a metallic plate, which 

 is pierced with a circular opening, whose diameter subtends this 

 same number of seconds, and the portion of the luminous disc 

 which you will thus discover will be equal in size and in bright- 

 ness to the sun as seen from Uranus. Viewed from this planet, 

 the illuminating particles are removed to a distance from the 

 eye of 753 niillions of leagues. Observed from the earth, their 

 distance is nineteen times less, or only 39 millions of leagues. 

 The difference is enormous ; but it is also to be observed, that, 

 in the first case, all the points of the surface of the sun, without 

 exception, send their light to the eye ; whilst, in he experi- 

 ment made from the earth with the metallic screen, we per- 

 ceive through the opening only a very small portion of the lu- 

 minary. I have already demonstrated that the compensation is 

 perfect *. 



These premises then being established, let us see how they 

 can serve to decide the question, whether the light of comets is 

 an emitted or a reflected light ? 



IjCX. us first prove, that, as to the equality of the intensity, 



• In this demonstration I have considered only plane surfaces. The law- 

 is not less true with regard to curved ones ; but I cannot prove it witliout 

 entering into details which would extend this article much too far. 



