1886.] on Telescopic Objectives and Mirrors. 415 



Larger sizes, which are polished on the surfaces, can be more 

 easily examined. It is difficult to describe the appearances, but I will 

 put a few discs into the lantern polariscope and endeavour to point 

 out what amount of polarization may safely be permitted in discs of 

 glass to be used for objectives. 



The composition of metallic mirrors of the present day differs 

 very little from that used by Sir Isaac Newton. Many and different 

 alloys have been suggested, some including silver or nickel or arsenic ; 

 but there is little doubt that the best alloy, taking all things into 

 account, is made with 4 atoms of copper and 1 of tin, which gives the 

 following proportions by weight : copper 252, tin 117*8. 



Calculation op CtrEVES. 



Having now obtained the proper material to work upon, the first 

 thing necessary is to calculate the curves to give to the lenses, in 

 order that the objective, when finished may be of the required 

 focus, and be properly corrected for the chromatic and spherical 

 aberrations. 



As this lecture is intended to deal principally with the technical 

 details of the process, I do not intend to occuj^y your time for more 

 than a few moments on this head, nor indeed is it at all necessary. 

 In my lecture last Saturday I explained the principles of achro- 

 matism, and in many published works full and complete particulars 

 are given as to the calculation of the curves — particulars which are 

 sufficient, and more than sufficient, for the purpose. 



Much has been discussed and written concerning the calculation 

 of curves of objectives, and much care and thought has been be- 

 s^^owed by mathematicians on this subject, and so far as the actual 

 constructors are concerned, a certain amount of veil is thrown over 

 this part of the undertaking, as if there were a secret involved, and 

 as if each had discovered some wonderful formulas by which he was 

 enabled to calculate the curves much more accurately than others. 



I am sorry to have to dispel this illusion. Practically the case 

 stands thus. The calculation of the curves which satisfy the con- 

 ditions of achromatism and desired focus is a most simple one, and can 

 be performed by any one having a very slight algebraical knowledge 

 in a few minutes, provided the refractive indices and dispersive power 

 of the glass be known. Both Messrs. Chance and Feil supply these 

 data quite sufficiently accurately for small-size objectives. Speaking 

 for myself, I am quite content to take the figures as given by these 

 glass manufacturers for any discs up to 10 inches in diameter. If over 

 that size, I grind and polish facets on the disc and measure the re- 

 fractive and dispersive powers myself. 



The calculations of the curves required to satisfy the conditions of 

 spherical aberration are very troublesome, but fortunately these may 

 be generally neglected. 



Some years ago the Royal Society commissioned one of its mem- 

 VoL. XI. (No. 80.) 2 E 



