M. Arago on the Light of Comets. 28 



ject is proportioned to the number of luminous particles which 

 impinge upon it, we arrive at this important optical law, that 

 the illum'matiiig intensity of a point diminishes ichen the dis- 

 tances increase, in the ratio of their squares. 



Let us now proceed, from the consideration of a point with- 

 out sensible dimensions, to that of a luminous surface that is 

 somewhat extended. 



Every individual point of this surface will evidently act like 

 the isolated point on which we have been dwelling ; that is to 

 say, it will emit a light, the diminution of which will follow the 

 progression of the square of the distances. It is only necessary 

 to add, that, in all positions, a screen placed in the course of the 

 rays will receive a quantity which, compared with that which 

 would have arrived from a single point, will be proportional to 

 the numbers of the illuminating particles, or, in other words, to 

 the extent of the luminous surface. 



We have just been considering a single point, which emit- 

 ted upon the thousandth part of a square yard of surface 10,000 

 particles at the distance of 1 yard ; 2500 at 2 yards ; 1111 at 

 3 yards ; . . . at . . . ; 1 at 100 yards. Well then, if there exist 

 1000 similar radiating points at the same distance from our 

 screen, of the size of the thousandth part of a square yard, it 

 will, without doubt, be sufficient to ascertain the brightness of 

 this screen, to multiply by 1000, all the numbers of particles 

 in the above figures. This multiplication will in no degree 

 alter their proportions ; for, if the successive terms of a series 

 are the Jbti7ih, the ninth, the . . . , the ten-thousandth, of a cer- 

 tain given number, they will still be the fourth, the ninth, the 

 . . . , the ten-thousandth, when these terms, and the number with 

 which they are compared, shall have all become a thousandth 

 times greater. 



The illuminating property, therefore, of a luminous surface 

 is, on the one hand, proportional to its extent, or to the number 

 of the particles of which it is composed ; and, on the other, it va- 

 ries, like that of an isolated point, in the inverse ratio of the 

 square of the distances. 



Will any one now then be greatly astonished, if I affirm, 

 that, in spite of th\s law, or rather on account of it, a luminous 

 surface should appear to the eye to have the same intensity at 



