■Prof. Petzval on the Camera Obscura. 7 



ninium of t>, we readily find 



p=^/ P^ , andD = 0-072\/-.^; 

 ^ V 0-036 V 0036' 



consequently for red and violet light we have, respectively, 



p = 0-08 in., p = 0-06 in., 



D = 0-006 in., D = 0-004 in. 



Thus the aperture which here corresponds to the sharpest image 

 is about ^th of an inch, or a little more than seven tipies the 

 best aperture in the natural camera. Consequently the illumi- 

 nation of the image is increased in the ratio of 1 : 50 nearly, 

 though it still remains inferior to the ordinary c^iera in the 

 ratio of 1 : 648. At the same time, however, the sharpness of 

 the image has been considerably improved. In the uatm-al 

 camera the image of a point had a mean diameter of 0-04 of an 

 inch ; it is now diminished to 0-005. The sharpness of the 

 image therefore is now eight times greater than before, and in 

 this respect is only inferior to the ordinary camera in the ratio 

 of 1 : 22|. 



These not very important improvements in sharpness and illu- 

 mination have been dearly enough purchased; for although the 

 general faithfulness to nature has not been essentially impaired, 

 the difficulty of obtaining sharp images has been increased, on 

 account of the chemical and optical foci being now separated by 

 about a quarter of an inch. It is true that the difficulty here 

 alluded to might easily be overcome if the linear chromatic aber- 

 ration, dp of formula (4), and with it the distance between the 

 foci, were always the same ; for then it would suffice to place the 

 plate destined to receive the picture a quarter of an inch in ad- 

 vance of the ground-glass plate. But it must not be forgotten 

 that the formuhe (3) and (4) are true only when the incident 

 rays are parallel, in other words, when the objects arc at a great 

 distance. An object at a finite distance a from the lens gives an 

 image, not at the focal distance p, but at a distance « from the 

 lens, a, p, and a being connected by the well-known formula 



1=1-' (5) 



u p a ' 



If we differentiate this expression according to the index of re- 

 fraction, implicitly contained in p, we have 



^^«=-p-> (6) 



where da. represents the real linear chromatic aberration, which 

 differs from the dp of formula (4) the more, the greater the dif- 



