for a double Telescope Objective. 297 



80 per cent with moderate curves ; 3 and 24 by 90 per cent 

 with still smaller curvatures ; 3 and 22 form a combination 

 without chromatic aberration, but requiring rather deep curva- 

 tures ; 55 and 28 are also practically perfect, reducing the sec- 

 ondary aberration 98 per cent, but demanding somewhat deeper 

 curves than the last pair. 



If, however, we impose the condition that only permanent 

 glasses shall be employed, which is an obviously imperative 

 condition for a telescope which is to be used out of doors, the 

 range of choice is very greatly reduced. The only pair sug- 

 gested in the catalogue which is useful from this point of view 

 is of !Nos. 8 and 25. These give an improvement of 65 per 

 cent over the ordinary objectives, but require the values 

 A 8 =10"7 A 26 = — 8 '29 ; this combination would without doubt 

 be very useful if we had nothing better. The above table, 

 however, suggests at least two combinations which are better, 

 one, that of 30 and 37, which, like 8 and 25, requires unde- 

 sirably deep curves, but which gives an improvement of 98 

 per cent, and the other !Nos. 14 and 27 which yields an im- 

 provement of 94 per cent and demands the somewhat more 

 manageable curvature sums of 9*78 and — 7'24. 



The trustworthiness of the data of the catalogue is the only 

 further element which we need to consider, since all the above 

 conclusions rest upon them. There are three excellent reasons 

 for placing the highest confidence in them. In the first place, 

 emanating from so eminent a physicist as Professor Abbe they 

 can hardly, by any possibility, be subject to systematic errors, 

 which alone we have to fear. Secondly : If we arrange the 

 materials according to their optical properties as given in the 

 table above we find that they fall into groups suggested al- 

 ready by their chemical composition. Thirdly : In the various 

 glasses which I have accurately determined the data of the 

 catalogue are exactly what they pretend to be, that is, the errors 

 of the indices of refraction are confined to the fourth place of 

 decimals, and the differences of the indices to the fifth place. - \ 



Among the glasses in my possession are the Nos. 14 and 27, 

 which, according to what appears above, form a most advanta- 

 geous combination. Of these I made prisms, determined the 

 optical constants with great precision, and then calculated an 

 achromatic objective. There were two questions of interest 

 which could only be answered by trying the objective. They 

 were, first, whether secondary chromatic aberration reduced to 

 about one-twentieth of its ordinary value could be detected by 

 the eye : and second, how much the defining power of such an 

 objective would surpass that of the familiar type. Thus, al- 

 though after studying the prisms and computing the objective 

 no doubt as to the validity of the conclusions from the table 

 remained, it was highly desirable to try a telescope so con- 



