166 Transactions of the Society. 



Here m = 5, and p = 10. 



_5^ 



200 



20-25 



a = 2 4- -= 2-025; /=-°l 2 - = 2-883; 

 onn ' J 7.025 



/"' = — 20 ' 25 — 1-169 



^ " 15-25 + 2-076 '" 17-326 



d = 2-025 X 1'169 = 2-367. 



A trigonometrical trace shows that 8 = 5°— 57' and 8' = 6°— 1', 

 the difference between these being only 4', which is sufficiently accu- 

 rate. The value of d precisely satisfies equation (i.), therefore the 

 correct foci and lens distance have been found. 



// 



Fig. 44. 

 F 



> 



F' 



$ 



V 



Example 3. — An eye-piece of 40 power is required for a -J -in. 

 telescope of 60 in. focus. Kequired the foci and lens distance. 



Here m = 40 and p = 60. Then a = 2-005, /= 2 '865, 

 /' = 0-983, d = 1-971. 



The trigonometrical trace (rigidly performed) shows that the 

 value of 8 is 5° — 59', and that of 8' = 5° — 54' ; further, equation (i.) 

 is satisfied by the above values. 



Let us compute this eye-piece by the ordinary formulae found in 

 the text-books, then the following results will be obtained ; f = 3, 

 f = 1, d = 2. The trigonometrical trace shows that 8=5° — 

 43' and 8'= 6° -10', the difference being 27'. With the above 

 values for the foci, equation (i.) shows that d ought to be 2-051. 

 Therefore the condition neither for achromatism nor for equal de- 

 viations is satisfied. Of course the equivalent foci are the same in 

 both examples, but it is remarkable that there should be so great a 

 difference in the results when the value of p is so large. 



Finding the foci of the lenses and the distance between them is 



