E, M. NELSON ON DETERMINATION OF FOCI. 4G1 



therefore 



In order to be consistent with our title, this must be construed 

 into arithmetic. 



Multiply the magnifying power by the distance between the 

 image and the object, and call the product A. 



Add one to the magnifying power, and multiply the result by 

 itself, and call the product B. The focus is found by dividing A 

 by B. 



This last formula (vi.) is perhaps the most accurate of all apart 

 from the determination of the Gauss points. The only error 

 consists in the measurement of s, for m can be ascertained with 

 perfect exactness. The distance s in the case of a 9-inch-focus 

 lantern lens will probably be only 1^, too much ; this small 

 amount, if s is considerable, will hardly affect the final result. 



In microscope objectives the Gauss points are sometimes crossed 

 over ; in these cases s will be too small. The error would, how- 

 ever, seldom amount to half an inch ; then, if S were made 100 

 inches, the final error would not bo appreciable. A longer 

 distance than this might be selected for s with low powers. 

 Before concluding, we might for a moment give our attention to 

 ]), or the " back focus," a term we succeeded in getting rid of at 

 the beginning. It is sometimes useful in lantern and camera 

 work to know j>, but perhaps less so in the case of a microscopic 

 objective. 



By (iii.) we learn that ;? = - ; then, by substituting for d its 



value in (v.), we have 



Therefore, p, the " back focus," is the '' equivalent focus," increased 

 by a quantity equal to .-, viz., the focus divided by the magnifying 



power. The larger the magnifying power, the less will ;; exceed 

 /; thus, when the screen is at an infinite distance, the magnifying 



power also becomes infinite, and / = o ; therefore, 2^ is as small as 



m 



possible, and is equal to /. But, as the screen approaches the 

 * Chaa. R. Cross, M.M.J. Vol. 4. (1870) p. 151. 



