810 



Transactions of the Society. 



y = 5, and for the second type (a = • 15) i^ = 9 in round 

 numbers.* 



Combining these values with the figure of v assigned above for 

 the apertures 0-85-0 "90, we have obtained a numerical determina- 

 tion of three points of the series of apertures in the dry system ; 

 and we shall arrive at an approximate estimation for the inter- 

 mediate points by interpolating the values of v between the said three 

 points. The annexed tabular statement exhibits in the fourth column 



Proportion of Aperture and Focal Length in a Normal Series of 

 Dry Lenses. 



Numerical 

 Aperture, 



010 

 015 

 0-20 

 25 

 30 

 0-35 

 0-40 

 0-45 

 0-50 

 0-55 

 0-60 

 0-65 

 0-70 

 0-75 

 0-80 

 0-85 

 0-90 



Aperture 

 An file 

 (air). 



Total Power , 



Critical 

 , I Value of the 

 correspond- g^ gr-am- 

 ingto a. pii'fication. 



11-5 

 23-0 

 35-0 

 47-0 

 60-0 

 73-7 

 89-0 

 106-3 

 128-3 



N. 



53 



79-^ 

 lOG 

 132 

 159 

 185 

 212 

 238 

 265 

 291 

 317 

 343 

 370 

 397 

 423 

 450 

 476 



10-0 

 9-0 

 8-2 

 7-4 

 6-7 

 6-1 

 5-0 

 5-3 

 5 

 4 

 4 

 4 

 4 

 4 

 4 

 4 

 4 



Objective 



Power 

 required, 



[N]. 



Focal Length 



required, 



/• 



5-3 



8-8 



12-8 



17-9 



23-7 



30-4 



37-9 



45-0 



53-0 



60-6 



68-9 



78-1 



86-0 



94-4 



103-2 



112-4 



119-0 



mm. 

 47-2 

 28-4 

 19-4 

 14-0 

 10-5 



8-2 



6-6 



5-5 



4 



4 



3 



3 



2 



2 



2 



2 



2 



7 



1 



6 



2 



9 



65 



42 



22 



10 



the series of v which results from the data given above, if the inter- 

 polation is made by means of a parabolic curve. The third column 

 repeats the figures of the minimum total amplification N required 

 for the various apertures, according to Table I. ; the fifth column 

 shows the objective-amplification [N] which results from the corre- 

 sponding value of V ; and the sixth column gives the focal length 

 / which will afibrd that objective-power in every single case. 

 Ketaining fractions in the values of v and /, whilst the basis of the 

 calculation is not determinate, has of course no other purpose than 

 to prevent arbitrary leaps in the series of figures, which, 

 according to the nature of the case, must show a continuous 

 gradation. 



According to the observations from which the figures of v have 



* The observations mentioned above were made several years ago, 1874-5. 

 In the mean time nothing, however, has occurred which can have changed the 

 essential conditions in regard to the construction of dry lenses. 



