VOL. XLI.J PHILOSOPHICAL TRANSACTIONS. SQQ 



The radius of the concave surface of the lens, turned from the speculum, 

 viz. of KLM, = 6.7 inches. 



The thickness of the lens at the vertex lh = ^ of an inch. 



The aperture of the lens must be about -^ of the aperture of the speculum. 



HP, the distance of the focal point p from the point h, where the abovesaid 

 lens is to be placed, so as to correct the errors arising from the different refran- 

 gibility of the mys, and also the errors of the spherical figure, =: 2^^ inches. 



HR, the distance of h, the vertex of the lens, from r, the focus of the te- 

 lescope, = 6.8 inches. 



And if we suppose the diameter of the pupil of the eye to be -i- of an inch, 

 though it has not one certain measure; then the diameter of the greatest 

 aperture of the speculum, that can ever be of use, will be 6^ inches, nearly. 



The small plano-convex eye-glass o must always have one common focus 

 with the telescope, viz. the point r translated to r, by reflection from the base 

 of the prism n; for which reason it must retain, at all times, an equal and 

 invariable distance from the lens ghiklm ; which distance will be the focal 

 length of the said eye-glass + hr = hn -(- Nr, the distance of the lens from 

 the focus of the telescope r. 



The form and position of the prism n, and the contrivance of the other 

 parts necessary, will be much the same as in the Newtonian telescope. 



If the focal length of the eye-glass be -J- of an inch, the telescope will mag- 

 nify about '200 times. 



This telescope may be contrived in the Gregorian way, by using, instead of 

 a lens and prism, a small speculum spherically concave on one side, and con- 

 vex on the other ; but we think it not worth while to attempt this construc- 

 tion, as an investigation of the proportion between the two surfaces necessary, 

 in this small speculum, to unite the rays proceeding from the great one, into 

 one point, would be intricate, and the practice also very difficult; because a 

 little inaccuracy will, in this case, occasion errors much more considerable than 

 a like imperfection in the refracting lens. 



We have hitherto supposed the radius of the concavity greater than that of 

 the convexity; as being most convenient and useful, on several accounts, in 

 forming this kind of telescopes; however, it may be proper to remark, that 

 the same method may be used for correcting the errors of the speculum, when 

 the radius of its concavity is less than that of the convexity ; only the refract- 

 ing superficies of the lens, placed between its vertex and focus, will be convex, 

 and not concave, as in the former case. And there is another thing worthy 

 of remark, that the focus, or point p, where the most refrangible rays are col- 

 lected, will fall farther from the vertex of this speculum, than the focus of the 



