458 E. M. NELSON ON DETERMINATION OP FOCI. 



plicity. On this point we can join issue, by showing that it is not 

 so simple as the more accurate optical formula. The expression 

 *' more accurate " is used, because, to determine the quantities in 

 question with absolute accuracy-, when a projection lens, consisting 

 of two or more elements, is employed, would, notwithstanding the 

 simplicity of the computation, necessitate the knowledge of the 

 curvatures of each lens, as well as of the refractive indices of the 

 various glasses of which they are composed, data which are not 

 commonly available. 



The optical formula, which may be found in every book on 

 natural physics, and in the first page of every optical text-book, is 



l^l-'p ("^ 



where d is the distance of the image from the first Gauss point, and 

 p that from the second Gauss point to the object. 



Now, for the reasons stated above, the position of the Gauss 

 points* from which d and p are measured is usually unknown ; but, 

 as d is large compared with p, the percentage of error in the case 

 of each measurement is by no means the same ; thus, an error of 

 one inch in six or nine inches is a very different matter to that of 

 one inch in twenty feet. If, for example, there is an error, k, of 

 one inch in the measurement of the p side, and if m = 60, the error 

 on the d side would be mk or five feet ; while the same error of 



Jc \ . 



one inch on the d side would only amount to -or — - inch on the 



., m 60 



p side. 



It is clear, therefore, that we must somehow or other get rid of 



p, while the small error in the measurement of d may be allowed 



to stand. Fortunately, there is another quantity which can be 



measured with absolute accuracy, and that is the magnifying 



power, 7W, or the number of times the image is larger than the 



object ; this is expressed by the fraction — = w. (Of course, in 



the case of a camera lens, the object and image are transposed, so 

 that in this and all subsequent formulae, when only a camera lens 

 is in question, i will mean the object, and o its image on the ground 



* Professor Sylvanns Thompson and E. Abbe have designed instruments 

 for the determination of the position of the Gausa points. They are, how- 

 ever, expensive, and not likely to be within reach of the ordinary worker. 



