80 On the Focometry of Lens- Combinations. 



distance through which the combination is moved, and this 

 in the case given above is large, 113*8 cm. 



The method which I now propose is, first, to find 0. This 

 gives OPi, or x } , and OP 2 , or y 2 , and the magnification y i /x l . 

 Also, as was shown in my first paper, divides H^Hx 

 externally in a ratio equal to the value of the magnification, or 



gi _ OH 2 

 x x OHi 



Hi H'2 O H 2 H, 



The nodal slide is now turned about through two right 

 anodes, when H 2 and H x will occupy the positions H 2 ' 

 and Hi'. The combination must now be moved through 

 the distance Hj'Hg so as to produce an image on the screen 

 which is not displaced. Let this distance, which can be 

 easily measured, be d. Then, if H 2 H! = «, we have 



a= ^.^^i^H 2 H 1 . 



«i +-yi 



In the case above mentioned, x l is 142 cm. and y Y 9*4 cm. 

 A careful measurement of d gave, for these positions of the 

 object and image, 2*8 cm. 



132*6 

 Thus a = 28 .j^ =2-45 cm. 



Also, 0H 2 = ^ -0475 cm. 



0Hx= ^ = 2-625 cm. 



Hence H.Pi-142-2'625-139-375 cm. 



H 2 P 2 = 9-4- -175= 9-225 cm. 



And 1 = 1 _ _J__, 



/ 9-225 139-375 



or /=9'87. 



The focal length and the distance H 2 Hi have thus been 

 deduced from the measurements of three lengths, and the 

 actual positions of H 2 and Hj determined. 



