M. Arago on the Light of Comets. 29 



will therefore be expanded into volumes of the same form S, 

 8, 17, 28 times larger at the distance of the Earth, Mars, Ceres, 

 and J upiter. 



These spheres, diaphanous on account of their extreme length, 

 exhibit themselves in simple circles. It is in the apparent sur- 

 face of these circles that the same quantity of nebulous particles 

 appear successively sprinkled with greater or less uniformity. 

 The luminous intensity of the nebulosity will evidently vary in 

 the inverse ratio of its density, — will follow the law of the sur- 

 face of circles; in other words, that of the squares of their dia- 

 meters, or the squares of the numbers 1, 3, 8, 17, 28. 



I have already proved, that a comet which had inherent light 

 would not experience, at any distance in which it could be ob- 

 served, any other variations of density than those of which we 

 have already specified both the cause and the law. We have 

 now, therefore, in addition, only experimentally to examine if 

 these variations are sufficient to render the most brilliant comets 

 invisible, as soon as they have reached the orbit of Jupiter. 

 The following is the method in which the experiment should be 

 undertaken. 



A telescope should be selected which had a large opening, 

 and a feeble magnifying power, and with which the comet could 

 be observed during the whole duration of its appearance. So 

 much being ready, the day, for example, in which the star shall 

 be found distant from the sun, a space equal to a radius of the 

 orbit of Venus, it should be examined, first, as a point of com- 

 parison, with the most feeble magnifier, and then with magni- 

 fiers 3, 8, 17, 28 times stronger. During these experiments, 

 the same quantity of light, that, namely, which the unvarying 

 extent of the object-glass would admit of, — that, in short, which 

 the circular image of the comet depicted in the first experiment, 

 would be found successively spread out upon circles 3 times, 8, 

 17, 28 times, larger diameters than in the first of the observa- 

 tions. But is it not evident, that the diminutions of intensity 

 which these artificial dilatations will induce upon the luminous 

 matter of the comet, will be respectively equal to those which 

 result from the corresponding natural dilatations, which the star 

 undergoes in removing from the sun ? or, in other terms, that 

 the simple changes in the eye-glass cause the comet to pass, so 



