A PRACTICAL EXAMPLE AFTER GAUSS 



If it is required to find 

 the conjugate of a ray pass- 

 ing through three lenses on 

 an axis, two of the lense> 

 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 bv 

 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 fresli 

 set of cardinal points is de- 

 termined in this manner 

 for the three lenses. 



So also with four lenses ; 

 the cardinal points of each 

 pair being found, they are 

 combined by the same 

 formula?, 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 

 si m pie, and the denomina- 

 tors of the four equations 

 are all alike ; so, too, in 



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