162 Transactions of the Society. 



Lay off a distance AO, say 1 in.; then AV will be /tAO = 

 1 '5 ; next find r by (iii.) ; in this manner, multiply AO by ft and 



1 *5 



divide by fi + 1, thus -— - =0*6. Next divide the N.A. by fi, thus 



— .■ * o 



1*3 



— = -8666 ; this is the sine of 6, the semi-angle of aperture ; by a 



1*0 



table of natural sines we find that it corresponds to an angle of 60° — 4'. 

 From the point lay off the angle A H = 60° - 4' ; from the centre 

 C with radius C A = r = • 6 describe the circle. The front is therefore 

 constructed, and all rays proceeding from O will be aplanatically re- 

 fracted as if they had come from the point V. Now, in order to find 



d> we must divide 6 by a, thus , ' • = ■ 5777, which by the tables 



1*0 



of natural sines we learn is 35°— 18'. 



Some would no doubt prefer a more mathematical treatment than 

 that of drawing out the lens in order to determine its thickness, the 

 diameter of its front, and the working distance. In the triangle H C 

 call the angle H C 0, /3, and the side HO, t, and let the front of the 



lens cut A V in B. Then /3 = 180°- (0 + <j>)-b= r 4^/; the 



sin 6 



diameter of the lens front = 2 b sin 6 ; the working distance B = 



b cos ; and the thickness A B = p — B 0. In our example then the 



following will be the values of the above terms : ft = 84° — 38', b = 



• 689, diameter of front 1 • 195, working distance = ■ 344, thickness 



of front = 0'656. 



The Huyghenian Eye-piece. 



History. — I have not been able to ascertain the date of the appli- 

 cation of this eye- piece to a telescope, but it is highly probable that 

 the addition of a field-lens to a Microscope by Monconys in 1660 

 followed its introduction, and no chronological anachronism would be 

 occasioned by this supposition, as Huygbens would have been thirty- 

 one years old at that date. It may be mentioned that this eye-pipce 

 has also been attributed to Campani. upon what grounds 1 am unable 

 to say ; in this 'country, however, it is known as a Huygbens' eye- 

 piece ; it is also sometimes called a negative eye-piece, but Coddington. 

 writing in 1 830, says that he is ignorant of the reason. It should be 

 noted that Monconys' eye-piece, according to the published formula, 

 had a field-lens of shorter focus than the eye-lens, and a distance be- 

 tween the lenses equal to the focus of the eye-lens ; this eye-piece 

 therefore was more like that of Eamsden's than Huygbens' construc- 

 tion. Huygbens' sole aim in his eye-piece appears to have been the 

 enlargement of the telescopic field, and the only condition he intro- 

 duced was that the total deviation should be equally divided between 

 the two lenses. 



His selection of 3 : 1 for the ratio of the foci of these two lenses 



