46 



DR. K. A. SAMPSON ON A 



refracting d..ullrt. These are all reasonable amounts, so that we are now in 

 possession of a good approximation to a workable solution which corrects coma and 

 . urvature of the field, and leaves the figure of the great mirror to correct spherical 

 aberration. 



It only remains then to adapt this solution to include consideration of all the 

 secondary factors that have been left on one side. 



We must now turn to the question of achromatism in general. A thin corrector, 

 such as is contemplated on p. 37, is, among other properties, achromatic ; but when 

 the lenses are made thick and their unit points separated, as must be, to make the 

 system real, this property is lost in greater or less degree. With two lenses only it 

 is not possible to restore it completely. Reserving the quantities q, q' for adjusting 

 aberrations, we may alter the ratio k : kf from the value 1, but this gives only one 

 adjustable element, whereas there are two necessary conditions for achromatism 

 for any specified position of the object, namely, identical position for the image and 

 identical magnification. It is true that in the ordinary achromatised refractor, 

 consisting of a doublet, results are obtained with satisfaction of only a single 

 condition, but the achromatism secured is necessarily very imperfect for another 

 reason the imperfect rationality of the dispersions of the two kinds of glass 

 and this masks the neglect of the second condition. For the reflector, where we 

 aim at perfect achromatism, we must add a third lens to supply an additional 

 adjustable element. I shall now give the theory of complete achromatism at a 

 chosen point with three lenses of the same glass, separated by given distances. To 

 make all the lenses of the same glass secures achromatism for all colours if it is 

 attained for any two. The lenses are supposed thin, and the results must therefore 

 be considered merely as approximations, since the thickness will alter the positions 

 of their unit points as well as their focal lengths when a ray of different refractive 

 index is considered. But the approximation will be generally close, and an 

 illustration of how to make a complete adjustment will be given later. 



> lenses be placed at O,, 4 , 0, and produce images in succession at P 3 , P 8 , P 7 



" ln the ^ Then the 



