vfJVatyiral Philosophy. 145 



The statements concerning the brightness of the image, 

 made in different propositions of this chapter, are not legit- 

 imately proved ; for the number of rays received by the 

 pupil from any one point of the object may be increased, 

 and the brightness nevertheless diminished, — on account of 

 the increase of apparent magoitade. 



Props. 108, 110, and 111, assert unconditionally con- 

 cerning the magnifying power of mirrors, what is true only 

 in certain positions of the eye. If, for example, the object 

 be nearer a concave mirror than its principal focus, and the 

 eye be in the centre of concavity, the image, instead of 

 " appearing larger" than the object, as is asserted in prop. 

 108, will appear of the same magnitude; and if the eye be 

 brought still nearer the mirror, the image will appear the 

 smallest. 



Prop. 144. Schol. 1. "Of two refracting telescopes which 

 magnify equally, the shorter will give a more imperfect im- 

 age than the longer. For the image appearing equal in both, 

 but being farther from the object-glass in the longer than 

 the shorter, must be in reality larger or more magnified ; 

 whence the defect arising from the diiferent refrangibility of 

 the rays, will be more visible in the longer than in the short- 

 er telescope." — The statement with which this paragraph 

 begins is correct. The reasoning subjoined is evidently 

 erroneous, and leads to a conclusion the reverse of what 

 was first asserted. If two telescopes were exactly similar 

 in all their parts, differing only in size, it is manifest that the 

 imperfection of the image arising from unequal refrangi- 

 bility, would be the same in both. But the smaller would 

 have the disadvantage of rendering the object less bright, 

 in the duplicate ratio of the linear dimensions. To render 

 the brightness the same in both, the object glasses must be 

 made equal ; in which case the one of least focal distance, 

 being a greater portion of a sphere, would produce the most 

 imperfect image. 



Schol. 2. The account of achromatic lenses In this scho- 

 lium omits the essential circumstance on which the whole 

 explanation turns. We are told that a convex lens of crowa 

 glass is to be united with a concave one of flint glass in such 

 a manner that " the excess of refraction in the crown glass 

 may destroy the colour caused by the flint glass." Here 

 the student will naturally inquire, how the crown glass can 



V0L.III....N0. I. 19 



