Mr. Lubbock on the Double Achromatic Object Glass. 167 

 / 4 -/, = --06272 f t - 4 =-'22648 / 4 -«/ s +/s»= — 27544 

 — ~= —-0000884 (/>- /l J (/ 2 _/j)2 -s - -0085448 



(4 -■*) &-/* ='010249 (/ 4 - A j (/,_/•)» = -000301. 



The preceding values will be found to destroy the coeffi- 

 cient of y* in the expression for/4. The values of the radii 

 are taken from a very useful table given by Sir John Herschel 

 in the paper before alluded to. 



One advantage which seems to me to result from the form 

 into which the equations have been put in this short view of 

 the theory of aberration is the facility with which the thick- 

 nesses of the lenses and the interval between them can be 

 taken into account. For if A 1? A 2 , A 3 , A 4 , are measured, as 

 before, from the points at which the surfaces cut the axis re- 

 spectively, we have obviously 



j_ 7»-l 1 C 1 J_\fJ_ 1 ~\ 2 my* 



Ai *' mr Y + wiA + \5»A 1 AJ ^A, A J 2(m — I) 9 ' 

 or, for parallel rays, 



1 _ ra— 1 y 2 



A^ = mr x + 2^ l d (m^l) 2; 



and if t x be the thickness of the anterior lens, or the interval 

 between the intersections of the axis by the first and second 

 surfaces, 



1 m — 1 m 



A 2 " r 2 A t + /, 



+ /J_ * "If* 1 T ^+^'aV 



U 2 w^ + OJ \A 2 A^^J 2A 1 a (7w-l)2 • 



In Sir John HerschePs construction the interval between 

 the lenses may be made inconsiderable. In this case 



1 ?»'— 1 1 



+ ^r 



m r 3 m A 3 



, fj L%£± _ JL V m ' (A * +t ' Y ^ 



\w'A 2 A 2 J LA 3 A 2 J 2A, 2 (m'-l 3 9 

 and if t 2 be the thickness of the second lens, 

 _1 m' — l m 



, J_L_ i__ UJL L_V ™ /g (^+0*( A 3 .f/ 2 )y 



\a 4 w '(v/«)j1a4 a 3 +/J g^v-i) 8 ' 



