414 Transactions of the Society. 



The Measurement of N.M.P. 



Helmholtz then, having shown that resolving power depends 

 upon the numerical aperture or, as he terms it, the normal magni- 

 fying power, of the beam transmitted by the objective, proceeds to 

 suggest a mode of measuring this N.M.P. His plan is to use the 

 Eamsclen circle as a gauge. We have already seen (p. 410) that 

 the antipoint of the reverted beam through the Eamsden circle 

 projected on the image plane is of necessity the same as the anti- 

 point of the beam received from the objective, whether with or 

 without an eye-piece field-lens, for both the beam received and the 

 beam emitted by the image have necessarily the same divergence 

 angle. We set up the instrument then upon an object, and bring 

 it into perfect adjustment. We next observe the magnification of 

 the image and the diameter of the Eamsden circle. Taking this 

 observed diameter (expressed in mm.) for our numerator, and for 



denominator the arbitrary constant 3, we obtain a fraction -^, 



where m stands for the diameter as above defined of the Eamsden 

 circle, and by it we multiply the observed magnification. The 

 result is the normal magnifying power of the objective, which we 

 may thus express : 



M = f M (8) 



This is Helmholtz' proposed scheme of rating objectives. 



Digressing for a moment from the Helmholtz paper to say a 

 word upon the merit of this method as compared with the method 

 now in vogue of rating objectives by the numerical aperture as 

 read by an apertometer, I desire to draw your attention to the all- 

 important consideration that N.M.P. can be estimated and is esti- 

 mated, if properly ascertained, under working conditions ; whereas 

 for the purpose of an apertometer measurement the instrument is 

 pulled to pieces and set to work under conditions which wholly 

 destroy its power of fine performance. When an apertometer 

 is used the index flame may show a falling off in brightness, betray- 

 ing the gradual cutting down of the oblique pencils long before 

 the edge of the aperture is reached, but there is nothing in the 

 apertometer to show when this mutilation of the oblique beams will 

 begin seriously to impair the performance of the instrument. Of 

 the two conditions of fine resolution, the apertometer therefore 

 measures only one and that the less important of the two ; for 

 Mr. Nelson's experiments already referred to show that when 

 resolving power has been destroyed by cutting down the oblique 

 pencils by a diaphragm placed behind the objective, it may be 

 restored by cutting down all the beams, i.e. the central and oblique 

 together, by means of a diaphragm in front of the condenser, thus 



