22 M. Arago on the Light of Comets. 



solved, and I the more willingly publish my views, as they may 

 serve to correct the ideas, often incorrect, which even some as- 

 tronomers seem to have adopted, concerning the manner in which 

 the intensity of the light of these luminaries varies, on account 

 of their distances from the sun and the earth. I remark, that 

 certain measures of intensity, which in themselves should not be 

 of difficult calculation, seem capable of affording, on the first fa- 

 vourable occasion, a definite solution to this curious problem of 

 astronomy. I shall endeavour to present in this place the prin- 

 ciples, though somewhat abstruse, upon which this method is 

 founded. 



Let us then dwell for a little upon a point without sensible 

 dimensions > and in itself luminous. From such a point there 

 would emanate, in all directions, particles of light, which would 

 propagate themselves in straight lines. At the distance of a 

 yard these particles will be uniformly distributed upon the sur- 

 face cf a sphere, having its radius a yard long. At the dis- 

 tances of 2, of 3, of ... , of 100 yards, the same number of par - 

 tides, or, still more accurately, the same particles themselves, 

 gradually elongating themselves from their points of departure, 

 will come in contact with spheres of 2, of 3, of ... , of 100 

 yards radius. And the surface of these spheres will go on in- 

 creasing with the radii. It is, moreover, well known that this 

 increase is not in the ratio of the length of the simple radii, but 

 that it augments in the ratio of their squares, so that, at the dis- 

 tances 2, 3, 4, ... , 100, the surfaces are 4, 9, 16, . . . , 1000, 

 greater than the distance 1. Thus, it may be affirmed, not 

 only that the particles of light will be not nearly so close to- 

 gether, and that they will separate more and more as they de- 

 part further from the radiating points, but also, that this scat- 

 tering will follow the law of the squares of the distance. 



And what has now been predicated of the entire sphere must 

 be equally applicable to each of its parts. If at the surface of a 

 sphere of a yard radius, we allow, for example, 10,000 particles 

 upon the extent of a thousandth part of a square yard, there 

 will be, upon an equal extent, the fourth part, or 2500, at the 

 distance 2 ; the ninth part, or 1111, at the distance 3 ; the ten- 

 thousandth part, or 1 only, at the distance 100. And admit- 

 ting, as has been generally done, that the brightness of an ob- 



