SUMMARY OF CURRENT RESEARCHES. ■ 767 



measurements of deviation are also made more accurate by taking- 

 advantage of the two burrs thrown up by the engraving-tool on each 

 side of every division of the goniometer circle. These are so illuminated 

 as to appear as two fine white lines, and a quartz fibre being brought 

 over each in turn, the mean reading is taken. 



In order to get thoroughly representative figures for each glass- 

 melting (about 150 lb. weight), three pieces are chosen at hazard from 

 different parts of it, and these are made into prisms. The average 

 index is then taken as that of the melting, each prism having been 

 measured as to deviation as stated. 



Finally, the author checks the errors of his working instrument by 

 comparing the indices with those of a larger goniometer having an 

 18 in. circle and object-glasses of 3 in. aperture and 30 in. focus. 

 There is also a careful correction for temperature. By the method de- 

 scribed it is considered that another decimal place is gained. 



Prof. Hastings having long since given as his opinion* that the 

 inconsistencies in his results in the calculation of objectives made of 

 three separate glasses were due to want of accuracy in the refractive 

 indices, Mr. Clifford has made a comparison of the optical constants sent 

 out with the glasses by the makers with those found by his method as 

 well as with the results obtained with them. He finds that the triple 

 is so sensitive to variation of index that, in the case in point, if four 

 decimal places only, instead of five, are taken in the index, then the 

 focus of one of the component lenses, from being positive, becomes a 

 minus quantity. Hence it is quite imperative that the refractive indices 

 should be carried to as many decimal places as the accuracy of the 

 deviations warrants. 



Lines B, D, and G of the solar spectrum were used as a basis of 

 calculation for some of the earlier triples. Mr. Clifford uses B', a red 

 helium line, A, a lead fine, and 3>, the 6th cadmium line, the two latter 

 being respectively the visual and photographic maxima for rays which 

 have passed through the glasses used. By employing these he gets the 

 further advantage of shallower curvatures. 



The paper goes on to describe a lens actually constructed, and con- 

 cludes with an appendix giving the formula? for the first approximation 

 and for the trigonometrical trace of a ray, as well as a diagram of the 

 curve of focal lengths of the triple for the different wave-lengths as- 

 compared with those of a doublet. The trigonometrical trace is, with 

 very slight modifications, applicable to object-glasses for the Microscope. 



The following will illustrate the author's method of finding the re- 

 ciprocals of the foci for the apochromatic triple : — 



fx is baryta light flint ; /a' is borosilicate flint ; p" is borosilicate 

 crown. The differences of proportional spectra are : A' - D, 0* 00168 ; 

 I) - F, - • 00030 ; F - G', • 00805. The refractive indices are :- 



B', 7066 (He) A, 5607 (Pb) 4>, 4678 (Cd 6 ) 



/*! =1-569074 fx 2 =1-576104 /^ =1*584492 



fj.\ = 1 • 569909 fi 2 = 1 • 577675 /,/ 3 = 1 ■ 586869 



fx'\ = 1 ' 497250 /x" 2 = 1 • 502400 fi" s = 1 ■ 508:365 



* Amer. Journ.'Sei.'and Arts, xviii. p. 433. 



