E. M. NELSON ON DETERMINATION OF FOCI. 459 



glass.) Now, on that same first page of the oi3tical text-book 

 will be found another very elementary rule, which says that the 

 size of the image bears the same proportion to the size of the 

 object as the distance of the image from the lens does to the 



distance of the object from the lens— so — = — hut L = m. 



p 



Therefore 



d 

 "^=7 > (iii.) 



By (iii.) we are enabled to eliminate p from equation (ii.) by 



substituting — for it, and thus obtain a result that will be service- 



m 



able to us, viz. : — 



d 

 ^-^i ' (-) 



and 



d=/m+f. (v.) 



Let us take (v.) first. Here we see that, in order to find the 

 distance a lantern must be placed from a screen, it is only necessary 

 to multiply the magnifying power by the focus, and afterwards add 

 the focus. Example : — Find the distance a lantern lens must be 

 placed from a screen to give, with a 9-inch projection lens, a 12-feet 

 disc, the slide mask being 3 inches. 



The answer may be obtained by mental arithmetic in the follow- 

 ing manner : — 



As 3 inches is a quarter of a foot, the magnifying power with 

 that size of mask will always be four times the diameter of the disc 

 in feet. Therefore m := 12 x 4. Now, /, the focus, is three-quarters 

 of a foot, therefore f m is |xl2x4. The 4's cancel out, leaving 

 3 X 12, to which must be added the focus. The final result is 36 j 

 feet. If we require a 10-foot disc, with a 6-inch lens, we shall 

 have ^xl0x4, and, adding the focus, we obtain 20J feet, the 

 distance required. If we use a 12-inch projection lens, we have 

 only to multiply the disc in feet by 4 and add 1. 



It will now be probably admitted that the optical and more accu- 

 rate method when expressed in this form is as easy, if not easier, 

 than the less accurate geometrical, or pinhole, method, as given in 

 the text-books. But some may say that formula (v.) is the same 

 as (i.), with only the addition of the focus. This is perfectly true j 



JouRN. Q. M. C, Series II., No. 35* 32 



