40O PHILOSOI'HICAL TRANSACTIONS. [ANNO 1740. 



least refrangible a; a circumstance which never happens by refraction alone, in 

 glasses of any figure whatever, or however they be disposed. 



Now all things being put as before, and making fig. 5, Ha = d, then the 

 convex superficies ghi, of a lens placed at h, that shall correct the errors 

 arising from the different refrangibility of rays, in this kind of speculum, 

 will be part of a sphere, whose radius is = - , " ^ }, = <j. And hk, 



r r ' (/* — ni)d + n« ' 



the distance of the point r, where the rays of all sorts will unite, after this re- 

 fraction, from H the given point in the axis, will be = — — — — r^— - — ; which 

 point R being taken as a centre, describe on it the arch klm, and the figure 

 GHiMLK will represent the section of a meniscus-glass, or lens, which, placed 

 at the point h, assumed between the vertex and focus of the speculum, will 

 collect all sorts of rays proceeding from it, into one and the same point, or 

 focus K. We might also show, how this error may be rectified by one or more 

 glasses, placed in the axis, at a distance further from the vertex than the focal 

 point p ; but the former speculum is so much preferable to this, for the con- 

 structing of telescopes, that we think it not worth while to prosecute this 

 matter further. To conclude this essay ,• 



Whoever shall think fit to put the method here proposed in execution, we 

 dare venture, from a trial that has been made, to assure him of success ; pro- 

 vided the same diligence, care, and accuracy, be applied, in choosing, figuring, 

 polishing and foiling, the glass, that has of late been employed for the form- 

 ing speculums of metal ; and let none be discouraged, though the first and 

 second attempt should fail; for that must be expected, if the ordinary way of 

 grinding and polishing be used : greater exactness is here required, than is 

 usually thought sufficient for the object-glasses of refracting telescopes: let it 

 be also considered how many essays, for a long term of years, were made by 

 Mr. Gregory, Sir Isaac Newton, and others, to reduce their constructions of 

 the reflecting telescope into practice, without answering, in any tolerable de- 

 gree, what their theories promised : the workmen they employed were chiefly 

 optical instrument-makers, and had it been left to such persons only to per- 

 form by themselves, we have reason to think, that it would have been pro- 

 nounced impracticable to this day, to make a reflecting telescope that should 

 equal or excel refracting ones of 10 times its length; though we now see, that 

 most of these artificers are capable of making them to such a degree of per- 

 fection as was formerly despaired of. 



April 5, 1739. 



I 



