Dr. Wollaston^s Microscopic Doublet. 257 



Par. 5. " My experience has led me to prefer a lens of a plano-convex 

 foiTO, even when made of glass; but the sapphire lens of this form, 

 recently introduced into use by Mr. Pritchard, has a decided superiority 

 over every single lens hitherto employed." 



As experience is but a blind guide in the science of optics, 

 it would be much more satisfactory if Dr. WoUaston would 

 condescend to assign some reason for what he asserts, if not to 

 prove his propositions. Mr. Herschel, in his treatise on light, 

 has been so obliging as to favour us with the reason why a plano- 

 convex lens of sapphire, or other substance of equally refrac- 

 tive power, is the best figure for bringing parallel rays to a 

 focus, when its convex side is opposed to them, or, by conse- 

 quence, for causing diverging rays impinging upon its plane 

 surface to emerge parallel *. Had Dr. Wollaston chosen to 

 prove mathematically the superiority of a sapphire lens over 

 a glass one, the same reasoning would also have served to 

 prove the equal superiority of a diamond one, of proper figure, 

 over the sapphire, in point of lower spherical aberration f , 

 though it is certainly true, that the dispersive power of sap- 

 phire is lower than that of diamond. No substances are pre- 

 sented to us by nature crystallized in such a variety of forms 

 as"^ diamonds, by far the greater number of which are unfit 

 for optical purposes, having two axes of polarization : some 

 stones are, however, occasionally met with, totally free from 

 all traces of double refraction ; some, again, have a double 

 refraction, but this can be got the better of, as in the case of 

 the sapphire, by causing the axis of the lens to coincide 

 with that of the stone. 



-'W^. Cornelius Varley has a partly polished plano-convex 

 diamond lens in his possession, which has no double refraction 

 about it. Mr. P. has a perfect double convex, which has been 



• Encyclopscdia Metropolitana, pi. 19, p. 388. Article, Light. 



306. If ^ =r 1 .6861, as is nearly the case with several of the precious stones, 

 and the more refractive glasses, R" = o ; and the most advantageous figure for 

 collecting all the light in one plane, is plano-convex, having its convex side turned 

 to the incident rays. 



-f- I take the liberty of extracting from Mr. Coddington's invaluable work a 

 note to page 110, to shew how very rapidly aberration decreases with an increase 

 of refractive power, at least with a lens of the best figure : the refractive index of 

 sapphire is 1 .764, that of diamond as high as 2.755. 



" The following are values of the complete coefficient of y', which we may re- 

 " present by u for diiferent values of (a. I have also inserted the best ratio of the 



