46d E. M. NELSON ON DETERMINATION OF FOCl. 



but we reply, first, tliat the simplification given above, viz., that of 



employing the terms /w in place of their equivalents, 



uiasK. 



has never even been hinted in the text-books ; and, secondly, that 



the argument by which fm +/ is obtained is based on true optical 



principles, and by no manner of means could it have been evolved 



out of the pinhole method. 



There is yet another erroneous statement which one often meets 

 with in connection with the pinhole treatment of the subject : this 

 is, that " double the size of the disc is obtained by doubling the 

 distance of the lantern from the screen." Careful measurements 

 will show that it is not the fact. The optical formula states that 

 it is necessary to subtract the focus after doubling the distance. 

 Example : — With a 9-inch projection lens, a 10-foot disc is 

 obtained at a distance of 30 feet 9 inches. What distance will be 

 required for a 2 0-feet disc? Double 30 feet 9 inches is 61 feet 

 6 inches. Less the focus is 60 feet 9 inches, the correct distance. 



To ascertain the focus of a lens — be it a microscope objective, or 

 lantern projection lens, or ordinary camera lens — the procedure is 

 equally simple. Care must be taken to make enlarge, then all that 

 Aeed be done is to divide d by the magnifying power plus one 

 (formula iv.). Thus, if the magnifying power is 40, and d is 20 J 



feet, /=^^*=i foot. 



The above arithmetical results are sufficiently accurate for 

 lantern and other general purposes ; nevertheless, some of our 

 members would perhaps prefer an alternative and more mathema- 

 tical treatment of the subject, and yet one which would not involve 

 the trouble of procuring the necessary data required for the 

 calculation of the Gauss points. Let s be the distance between i 

 and 0, viz., between the screen and the slide. Then s = d -{■ p, 



and, by (iii.) above, i? == - ; combining these, we have 

 hi 



ms 



m -^ I 



but by (v.) 



J=/(,;z+l) 

 then 



ms ' 



f(m^ 1) = 



