A PEACTICAL EXAMPLE AFTEK GAUSS 



If it is required to find 

 the conjugate of a ray pass- 

 ing through three lenses on 

 an axis, two of the lenso 

 must be combined and their 

 four cardinal points found. 



The principal points 

 and the focal length of the 

 third lens must then be 

 calculated, and then com- 

 bined in their turn by 

 formula (ix), (x), (xi), and 

 (xii), p. 116, with the car- 

 dinal points of the double 

 combination. 8 is taken as 

 the distance of the first 

 principal point of the com- 

 bination, nearest the third 

 lens, to the second principal 

 point of the lens, nearest 

 the combination. A fresh 

 set of cardinal points is de- 

 termined in this manner 

 for the three lenses. 



So also with four Irn.-o : 

 the cardinal points of each 

 pair being found, they are 

 combined by the same 

 formulae, and new cardinal 

 points for the whole com- 

 bination of four lenses arc 

 obtained. Similarly, the 

 cardinal points of five, six, 

 or any number of lenses 

 can be found and the con- 

 jugate of any point localised. 



Finally, no one need be 

 discouraged by the appear- 

 ance of the length of the 

 calculation ; the example is 

 given in full, so that any 

 one acquainted only with 

 vulgar fractions and deci- 

 mals can work it, or any 

 other similar problem, out. 



In lens No. 1, for in- 

 stance, the numerators of 

 the fractions are all very 

 simple, and the denomina- 

 tors of the four equations 

 are all alike ; so, too, in 



v 



