1834.] Miscellaneous. 309 



all objects surrounding it. In the next place, let us imagine another cylinder, a 

 hollow one, to be placed concentric with the former, but at such a distance on the 

 outside of it, that any object situated on the inner surface of the outer cylinder, 

 may be distinctly reflected upon the outer surface of the inner one. 



Now as every particle in the outer cylinder is reflected from that part of the 

 inner one which is situated immediately and perpendicularly opposite to it, it is 

 evident that the whole of the outer cylinder is represented on the polished surface 

 of the inner one, but the latter being on account of its interior situation the smal- 

 ler of the two, it follows that every object that is situated on the inner surface of 

 the outer or larger cylinder, must be represented on a smaller scale (as far as its 

 lateral measurement is concerned) upon the polished surface of the inner and 

 smaller one, than it really is in the other, which contains the real size or dimen- 

 sions of the object. 



It may be easily seen then, that if a polished globe or a polished segment of a 

 circle similar to a convex mirror be substituted for the inner cylinder, the same 

 reasoning must hold good, for each dimension of the image, in which case the 

 reflected objects must become diminished both in height and diagonal measure- 

 ment, as well as breadth, merely because the surface upon which they are repre- 

 sented is less than that of the objects themselves. 



So much for the reduction of the spectrum or image of objects in convex mirrors, 

 and as to the increase of it in concave ones, the reasoning must be exactly the 

 same, as for the above, excepting that the object must then be considered as 

 situated on the outer surface of the inner cylinder, which should be unpolished, and 

 be reflected from the inner polished surface of the outer one, in a magnitude of 

 course greater than the object itself, in proportion to the increased radius of the 

 outer mirror. 



I cannot but express a difference with the common opinion, that the place of 

 the spectrum in the convex mirrors is at H., see the accompanying figure numbered 

 in Hutton, fig. 30, plate 9 ; it may surely with fairness be considered to be at M., 

 that is exactly at the same distance within the mirror measured on the prolonga- 

 tion of the line of reflection, as the object is distant from the point of incidence, 

 in the same manner as in a plane mirror ; for although the object or rather its 

 image arrive at the eye in a reduced size when reflected from the convex mirror, 

 yet by the above reasoning, with the two cylinders, it is easily explained, for the 

 image of the object, having fallen from without upon the convex surface of the mir- 

 ror which is situated within and which in this case corresponds as it were with the 

 inner cylinder above noticed, has become itself reduced in size, and being so reflect- 

 ed, proceeds towards the point of sight in that diminished state, and therefore it 

 necessarily appears to the eye when reflected from the convex mirror less in size 

 than it really is, and by a parity of reasoning, greater in size when reflected from 

 a concave one. 



In my opinion, the image (with the exception above noted of its being reduced 

 in size, by its actual contact with the speculum without the eye having any thing to 

 do with that reduction) is not only situated at the same distance above described 

 within the mirror, as the object is distant from the point of incidence, but it 

 becomes reflected from a convex mirror in exactly the same manner that it would 

 be from the polished surface of a plain one, such as F. G. where the angles B. E. 

 F. A. E. G. formed by the lines of incidence and reflection, B. E. E. A., with the 

 speculum are always equal to one another. 



