Mr. Lubbock on the Double Achromatic Object Glass. 169 



from the conditions of achromaticity and the equation to de- 

 termine f 9 after the numerical substitutions, is 



f£ -f -40766^ = — -01377, which equation gives 



f 3 = — -03716 or — -37050. 



Froin/3 = —03716, I find 



r 3 = 3-0573 and r 4 = 14-151, 



instead of r 3 = 3*0640 and r 4 = 14*297, which were the 

 values of those quantities when the thickness of the double- 

 convex lens was neglected. The difference in the values of 

 the radii corresponds in each case to the indication -0007 inch 

 by a spherometer of 5-inch radius, which might be apprecia- 

 ble in large telescopes, but not, I apprehend, in common in- 

 struments. 



In the last example I have neglected the interval between 

 the lenses : if this be taken into account and the thicknesses of 

 the lenses be neglected, it is evident that for parallel rays 



1 m — 1 y 2 



+ 



«y 



A, " mr x T 2A 1 3 (ro-l)* 



A 2 r 2 T A, r I A 2 mAj X A 2 A, J 2(ot-1) ( 



If the interval between the lenses be called t 2 , 



JL - m '~' 1 1 



A 3 " m'r 3 w'(A 2 + * 2 ) 



, / J LI J L + 1 y m>(A 2 +t,y 



* \m'A 3 A 2 + / 2 J I A 3 r _ A 2 -f tj 2V(w'-l) 9 •* 



1 m'— 1 m' 



+ 



A4 >4 <*3 



+ lA 4 W 'A 3 J \A 4 Aj 2A 2 >'_1)^' 



The condition of achromaticity gives 



Retaining the previous curvatures of the flint lens, and the 



values of — and — in the term multiplied by t 29 it is easy 



A 2 A 3 



to calculate the influence which the consideration of the in- 

 terval between the lenses has upon the curvatures which 

 should be given to the double-convex lens. 



Third Series. Vol. 7. No, 39. Sept. 1835. Z 



