VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. 8p7 



Seeing therefore it is possible, and we believe also practicable, to remedy the 

 imperfections of this kind of speculums, from whatsoever cause they arise, by 

 the method we have here proposed ; it seems to follow, that catodioptrical te- 

 lescopes may be carried, by this means, to as great a degree of perfection, as 

 they are capable of receiving ; provided spherical figures can be truly given, 

 with an exquisite polish, to glasses of a large aperture, and a foil of quicksilver 

 made also to retain that figure accurately, and without any inequality ; for the 

 object glass or speculum being rendered perfect, so as that all sorts of rays, 

 proceeding from one lucid point in its axis, shall be collected by means of the 

 lens exactly in another point, its aperture may then be extended to its furthest 

 limits ; and that is, till the whole pupil of the eye, or the whole portion of 

 the eye-glass to be used, when that becomes necessarily less than the pupil, 

 be filled with rays proceeding from the speculum, and flowing from one point 

 of the object, but no farther; because this is a limitation made by nature in 

 the structure of the eye itself : and in telescopes whose construction is such as 

 we have now described, the largest aperture of the speculum that can ever be 

 of use, will be to the diameter of the pupil of the eye, very nearly, in a ratio 

 compounded of the ratios of the focal length of the speculum, to the distance 

 of that focus from the lens, and of the distance of the lens from the focus of 

 the telescope, to unity : that is, of bp to ph, and of kh to ) ; which proportion 

 holds, whatever be the charge or the power of magnifying. 



But if inquiry be made as to the charge most proper and convenient, that 

 will be best determined by experience, in these, as well as in all other sorts of 

 telescopes : however, on supposition that one of a given length has its aperture 

 and charge rightly ordered and proportioned, the rule for preserving the same 

 degree of brightness and distinctness, in all others of a like construction, will 

 be, to make the apertures, and magnifying powers, directly as the focal lengths 

 of the speculums; which shows the vast advantage and perfection of these te- 

 lescopes, above the common reflecting ones; where, according to Sir Isaac 

 Newton's rule, the apertures, and powers of magnifying, must be as the bi- 

 quadrate roots of the cubes of their lengths. See his Optics, 2d edition, 



P- 97- 



It is likewise a considerable advantage in this construction, that the reflection 

 from the concave side of the speculum will do no sensible prejudice; because 

 the image of any object there made, is removed to so vast a distance from the 

 principal image, formed by the convex surface, as to create no manner of con- 

 fusion or disturbance in the vision ; which necessarily happens, in some degree, 

 from the vicinity of those images, when the glass is ground concave on one 



