TELESCOPES. 71 



fixed stars, since they convey a greater quantity of intense 

 light to the eye without perceptibly enlarging the image ; 



age when seen by the naked eye by dividing the square of the diameter 

 of the object-glass by the square of Ike diameter of the emerging pencil, or 

 rather the surface of the object-glass by the surface of the circular base 

 of the emerging pencil. 



" By dividing the surface of the object-glass by the surface of the pu 

 pil, we have already obtained the ratio of the total quantities of light 

 produced by the two images of a planet. This number is lower than 

 the quotient which we obtain by dividing the surface of the object- 

 glass by the surfafce of the emerging pencil. It follows, therefore, with 

 respect to planets, that a telescope causes us to gain less in intensity of 

 light than is lost by magnifying the surface of the images on the retina; 

 the intensity of these images must therefore become continually fainter, 

 in proportion as the magnifying power of the telescope increases. 



"The atmosphere maybe considered as a planet of indefinite dimen- 

 sions. The portion of it that we see in a telescope will therefore also 

 be subject to the same law of diminution that we have indicated. The 

 relation between the intensity of the light of a planet and the field of at- 

 mospheric light through which it is seen, will be the same to the naked 

 eye and in telescopes, whatever may be their dimensions and magnify- 

 ing powers. Telescopes, therefore, do not favor the visibility of planets 

 in respect to the intensity of their light. 



" The same is not the case with respect to the stars. The intensity 

 of the image of a star is greater when seen with the telescope than with 

 the naked eye ; the field of vision, on the contrary, uniformly illumined 

 in both cases by the atmospheric light, is clearer in natural than in tel- 

 escopic vision. There are two reasons, then, which, in connection with 

 the consideration of the intensity of light, explain why the image of a 

 star preponderates in a telescope rather than in the naked eye over that 

 of the atmosphere. 



" This predominance must gradually increase with the increased 

 magnifying power. In fact, deducting the constant augmentation of 

 the star's diameter, consequent upon the different effects of diffraction 

 or interference, and deducting also the stronger reflection experienced 

 by the light on the more oblique surfaces of ocular glasses of short focal 

 lengths, the intensity of the light of the star is constant as long as the 

 aperture of the object-glass does not vary. As we have already seen, 

 the brightness of the field of view, on the contrary, diminishes inces- 

 santly in the same ratio in which the magnifying power increases. All 

 other circumstances, therefore, being equal, a star will be more or less 

 visible, and its prominence on the field of the telescope will be more 

 or less marked, in proportion to the magnifying powers we employ." 

 Arago, Manuscript of 1847. 



I will further add the following passage from the Annuaire du Bu- 

 reau des Long, pour 1846 (Notices Scient. par M. Arago), p. 381 : 



" L'experience a montre que pour le commun des homines, deux 

 espaces eclaires et contigus ne se distinguent pas l'un de l'autre, a inoins 

 que leurs intensites comparatives ne presentent, au minimum, une dif 

 ference de $-$. Quand une lunette est tournee vers le firmament, son 

 champ semble uniformement eclaire : c'est qu' alors il existe, dans un 

 plan passant par le foyer et perpendiculaire a l'axe de l'objectif une 

 image indefinie de la region atmospherique vers laquelle la lunette est 

 dirigee. Supposons qu'un astre. c'est-a-dire un objet situfe bien au- 



