14 PHILOSOPHICAL TIlAJfSACTIONS. [anNO idj'l. 



cerncd for an hypothesis than I expected ; yet I doLibt not but we have one 

 common design ; I mean a sincere endeavour after knowledge, without valuing 

 uncertain speculations for their subtleties, or despising certainties for their 

 plainness: and on confidence of this I make this return to his discourse.* 



The first thing that offers itself is less agreeable to me, and I begin with it 

 because it is so. The considerer'}" is pleased to reprehend me for laying aside 

 the thoughts of improving optics by refractions. If he had obliged me by a 

 private letter on this occasion, I would have acquainted him with my successes 

 on the trials I have made of that kind, which I shall now say have been less 

 than I sometimes expected, and perhaps than he at present hopes for. But 

 since he is pleased to take it for granted, that I have let this subject pass with- 

 out due examination, I shall refer him to my former letter,;]: by which that con- 

 jecture will appear to be ungrounded. For, what I said there, was in respect 

 of telescopes of the ordinary construction, signifying, that their improvement is 

 not to be expected from the well-figuring of glasses, as opticians have imagined; 

 but I despaired not of their improvement by other constructions ; which made 

 me cautious to insert nothing that might intimate the contrary. For, although 

 successive refractions that are all made the same way, do necessarily more and 

 more augment the errors of the first refraction ; yet it seemed not impossible 

 for contrary refractions so to correct each others inequalities, as to make their 

 difference regular ; and, if that could be conveniently effected, there would be 

 no further difficulty. Now to this end I examined what may be done, not only 

 by glasses alone, but more especially by a complication of divers successive 

 mediums, as by two or more glasses or crystals, with water or some other fluid 

 between them ; all which together may perform the office of one glass, espe- 

 cially of the object-glass, on whose construction the perfection of the instru- 

 ment chiefly depends. But what the results in theory or by trials have been, I 

 may possibly find a more proper occasion to declare. 



To the assertion, that rays are less truly reflected to a point by a concave, 

 than refracted by a convex, I cannot assent; nor do I understand, that the focus 

 of the latter is less a line than that of the former. The truth of the contrary you 

 will rather perceiv-e by this following table, computed for such a reflecting con- 

 cave, and refracting convex, on supposition that they have equal apertures, and 

 collect parallel rays at an equal distance from their vertex ; which distance being 

 divided into 1 5000 parts, the diameter of the concave sphere will be 60000 of 



* Which discourse was thought needless to be here printed at length, because in the body of this 

 answer are to be met with the chief particulars, wherein the answerer was concerned. (Original.) 

 "t Mr. Hook. 

 X Printed in Number 80, of these tracts. 



