4g pi:. R A. SAMPSON ON A 



= -'01056, *= -1-3704. 



This is an illustration of the simple corrector (,,-* in contact) modified by a slight 

 separation of the two lenses and completed by the addition of a weak lens at a 

 considerable distance, and adjusted for a point which is nearly at the principal focus 

 , ,f t he middle lens. The exact solution on pp. 51-53, gives 



,,= -'01152, *.= - 1-3459; 



the differences are considerable ; this must be expected because the thicknesses of the 

 lenses are of the same order as the separation d, of the unit-points ; but in all cases the 

 solution will be close enough to supply a good approximation that will allow the actual 



case to be adjusted. 



The general process, suitable for use when we have obtained an approximation by 

 the method just explained, will be the following. Let the standard scheme and that 

 of the varied refractive indices be 



{G, H; K, L} and {G+AG, H + AH; K+AK, L+AL} 



respectively. Then the conditions for complete achromatism at the principal focus 



are simply 



AG = 0, AK = 0, 



for these imply that the focal length is unchanged and also the distance G/K from 

 the origin to the principal focus for either way. Then using the approximation 

 already supposed found, calculate the values of AG, AK which it shows. Vary the 

 focal length of the first lens and recalculate them. Vary also the third lens and 

 recalculate them. We then have means for interpolating the correct values of the 

 first and third lenses requisite to give an achromatic system in conjunction with the 

 middle lens. 



This will be illustrated by the calculation of the actual system which I set out to 

 tii id and to which I now come. It will be understood that it was obtained by steps 

 of approximation. 



It is unnecessary to give details regarding all these steps, which were unnecessarily 

 circuitous, owing to numerical mistakes and ill-judged processes. I shall therefore 

 give the final stage only. 



The notation is slightly varied from the standard notation of SEIDEL, is the 

 vertex of the great mirror, B its curvature, O a the vertex of first surface of the 

 reverser, O', the vertex of the second or silvered surface, 0".,, which is the same point 

 as O is the last surface of the reverser ; B s , B'.,, B" 2 = -B 2 , are the corresponding 

 curvatures ; 4 , (y 4 are the vertices of the first and second surfaces of the first lens 

 of tin- corrector, with curvatures B 4 , B' 4 ; O, 0' 6 with curvatures B 6) B' 6 refer to 

 the second lens of the corrector. For the thicknesses of the lenses I employ here 



