682 PHILOSOPHICAL TRANSACTIONS. [aNNO iS/l. 



that perfection they are now at. For measuring the refractions in one of my 

 prisms, I found, that supposing the common sine of incidence upon one of its 

 planes was 44 parts, the sine of refraction of the utmost rays on the red end of 

 the colours, made out of the glass into the air, would be 68 parts, and the sine 

 of refraction of the utmost rays on the other end 6g parts : so that the differ- 

 ence is about a 24th or 25th part of the whole refraction; and consequently, 

 the object glass of any telescope cannot collect all the rays which come from 

 one point of an object, so as to make them convene at its focus in less room 

 than in a circular space, whose diameter is the 50th part of the diameter of its 

 aperture ; which is an irregularity, some hundreds of times greater than a cir- 

 cularly figured lens, of so small a section as the object glasses of long telescopes 

 are, would cause by the unfitness of its figure, were light uniform. 



This made me take reflections into consideration, and finding them regular, 

 so that the angle of reflection of all sorts of rays was equal to their angle of 

 incidence ; I understood that by their mediation optic instruments might be 

 brought to any degree of perfection imaginable, provided a reflecting substance 

 could be found, which would polish as finely as glass, and reflect as much 

 light as glass transmits, and the art of communicating to it a parabolic figure 

 be also attained. But there seemed very great difficulties, and I have almost 

 thought them insuperable, when I further considered, that every irregularity 

 in a reflecting superficies makes the rays stray 5 or 6 times more out of their 

 due course, than the like irregularities in a refracting one : so that a much 

 greater curiosity would be here requisite, than in figuring glasses for re- 

 fraction. 



Amidst these thoughts I was forced from Cambridge by the intervening 

 plague, and it was more then two years before I proceeded further. But then 

 having thought on a tender way of polishing, proper for metal, whereby as I 

 imagined, the figure also would be corrected to the last ; I began to try what 

 might be effected in this kind, and by degrees so far perfected an instrument 

 (in the essential parts of it like that I sent to London,) by which I could dis- 

 cern Jupiter's 4 concomitants, and showed them divers times to two others of 

 my acquaintance. I could also discern the moon-like phase of Venus, but 

 not very distinctly, nor without some niceness in disposing the instru- 

 ment. 



From that time I was interrupted till this last autumn, when I made the 

 other. And as that was sensibly better then the first (especially for day objects,) 

 so I doubt not, but they will be still brought to a much greater perfection 

 by their endeavours, who, as you inform me, are taking care about it at 

 London. 



