92 COSMOS. 



light of the fixed star and of the aerial field or the mass of air 

 which surrounds the star in the telescope. Planetary discs 

 present very different relations from the simple ray of the 

 image of a fixed star ; since, like the aerial field (fair aerienne], 



contracted on emerging from the eye-piece. The diameter of 

 the first cylinder is to that of the second as the focal distance 

 of the object-glass is to the focal distance of the eye-piece, 

 or as the diameter of the object-glass is to the diameter of 

 the part of the eye-piece covered by the emerging rays. The 

 intensities of the light in these two cylinders (the incident and 

 emerging cylinders) must be to one another as the superficies 

 of their bases. Thus, the emerging light will be more con- 

 densed, more intense, than the natural light falling on the 

 object-glass, in the ratio of the surface of this object-glass to 

 the circular surface of the base of this emerging pencil. As 

 the emerging pencil is narrower in a magnifying instrument 

 than the cylindrical pencil falling on the object-glass, it is 

 evident that the pupil, whatever may be its aperture, will 

 receive more rays, by the intervention of the telescope, than 

 it could without. The intensity of the light of the stars will, 

 therefore, always be augmented, \vhen seen through a telescope. 



" The most favourable condition for the use of a telescope 

 is undoubtedly that in which the eye receives the whole of 

 the emerging rays, and, consequently, when the diameter of 

 the pencil is less than that of the pupil. The whole of the light 

 received by the object-glass then co-operates, through the 

 agency of the telescope, in the formation of the image. In 

 natural vision, on the contrary, a portion only of this light is 

 rendered available, namely, the small portion which enters 

 the pupil naturally from the incident pencil. The intensity of 

 the telescopic image of a star is, therefore, to the intensity 

 of the image seen with the naked eye, as the surface of the 

 object-glass is to that of the pupil. 



"The preceding observations relate to the visibility of 

 one point, or one star. We will now pass on to the conside- 

 ration of an object having sensible angular dimensions, as, 

 for instance, a planet. Under the most favourable conditions 

 of vision, that is to say, when the pupil receives the whole 

 of the emerging pencil, the intensity of each point of the 



