140 Mr. T. H. Blakesley on a 



lens-system, and let the points marked off at equal distances 

 (/) above the line be numbered in such away that the number 

 represents the relative size of the Object to the Image, when 

 the Object is placed in any one of the points, i. e. for the focus 

 of light before incidence, and let the points numbered below 

 the line,and also at equal distances (/]), bear a corresponding 

 series of numbers representing the relative size of Image and 

 Object when the Image is at any one of the points. 



Then any point represented by p on one of these scales is 



conjugate to the point represented by - on the other. The 



two principal foci must be marked and the two focal centres 

 must be marked 1. 



If the media at the ends are the same, the common distance 

 of the integral points will be the same in the two scales. 

 This condition, as being the common one, I shall assume to 

 exist unless the reverse is especially stated. 



The common distance between any two consecutive integral 

 points is the focal length ; and this is one important charac- 

 teristic of the system. Another characteristic is the aberration 

 of the integral points of one scale from those of the other. A 

 third is the order in which the numbers of the scales run 

 with reference to the direction of the light. 



It appears to me that two systems to deserve being called 

 equivalent one to the other should have coincidence in all 

 these three respects. If the top series has reference to light 

 before encounter with the system, and light is supposed to 

 come from right to left, then for a convex arrangement the 

 upper series of numbers increases in the same direction, i. e. 

 from right to left, and the lower series in the reverse direction ; 

 but for a concave arrangement these rules are reversed. 



It will be found that one of these diagrams will not be mis- 

 interpreted by turning it upside down. 



Hence in any combination it is necessary to find : — 



(1) The focal length. 



(2) Some point of known numerical denomination on 

 one scale. 



(3) Ditto for the other scale. 



With these three determinations all the facts connected 

 with image-formation as regards position and size may be 

 determined for any position of the object, and vice versa. 



The optical bank with which the focal length is determined 

 contains various sliding-pieces in a mahogany groove. Two of 

 them carry pieces for the support of the cells containing the 

 lens-combination, and two carry frames in which can be placed 

 photographs on lantern-plate glasses of evenly-divided scales. 



