by four readings. Then obviously n=— and /== ^ 



7 m 



i . m • , P m 



142 Mr. T. H. Blakesley on a 



ings. Then obviously n 



-, a very convenient form 



m + 1 • m — 1 



The slips of paper employed may be rolled up and stored, so 

 that reference can be made to them should occasion require it. 



The operation of finding the focal length of a concave lens 

 or combination is less important perhaps, but the following 

 general proposition may be of interest, and within limits may 

 be made applicable to any case. 



Suppose it possible to change the position of a portion of a 

 combination, so as to recover as in the last operation the same 

 pair of conjugate foci of that part of the combination. Then 

 clearly the focussing of the whole combination will be restored 

 to the same conjugate foci as before, though the magnification 

 will be changed. 



Let m be the factor of the total magnification due to the 

 moving portion, and let M be the total magnification : in the 

 first position M may be read off. i 



In the second position m changes to — , and M changes to 



N, say, which may also be determined. 



If K be the magnification-factor due to the stationary 

 portion of the combination, 



Km = M, - = N ; 



m 



from which m and K can both be determined, viz. 



M 



m 2 = ^, K 2 = MN. 



Hence the focal length of the moving part is 

 Im VMN 



or 



m 2 -l M-N* 



I have dealt with the finding of focal lengths before showing 

 how any particular focus may be found , with a view of accen- 

 tuating how completely independent the two matters are; but 

 it is clear that if any position of a pair of conjugate foci is 

 taken and the magnification is measured, one has only to 

 measure the distance of the scales from some fixed planes of 

 the lens-system (say the edges of the brass cells) in order to 

 allocate not merely the points for the particular magnification, 

 but for all magnifications both above and below the line. 

 Such measurements could easily be made by a sliding rule, 

 accurately to the tenth part of a millimetre ; but as the end 



