896 Mr. T. Smith on the Accuracy of the 



to the distances f and n are for the moment denoted by 

 F and N, 



p_l f -' /l 



These two expressions may if preferred be used in place of 

 the equations in (9) not involving a and b. 



The converse problem of designing a telescope to have 

 given constants may now be considered. It will be supposed 

 that /, n, B, 0, j3. 7 are given and that k, k\ and I are to be< 

 found. From (15) 



i(A+P)(C+ 7 ) - l + {B-£-(C + y)*'/*}/'/ 

 and i(A+Q)(C + 7 ) = l + {B-j8-(C+y>7*}/n. 



Also from (9) 



i(P+Q) = *7*(B-/3), 



and therefore 



B-i8-(C + 7)ir , /ic = Wj "> 



i(A-P)(C + 7) = y(W//), I 

 KA-QXC + 7) = y(l-*/n), 

 where > . . (16) 



y = A(C + 7 )-l 

 and 1 111 



< 7 "~B-/3 + /' l V j 



The second equation for C in (9) may be rewritten in 

 the form 



(A-P)(A-Q) = 4*w/(B-0), 



giving by (16) 



K \G+ y y =y{l + (B-fi)glfn\. . . (17) 



It is now possible to determine y hj substituting from (16) 

 and (17) in the relation implied by (13), with the result 



%{^(C-7) + 2(0/3+B 7 )}(B+ / 8){l+(B- i 8) 5 r/yn} 



= h(V+/3-¥o)+2f3}XC + y). (18) 

 When 7=0 the solution is 



^(B+/3) A</ B+,/5; 1 fa 



■frViB-PHP-e+falg)., 



