MICROSCOPES: ALFRED W. PORTER 71 



This is the least total mgignification necessary to reveal the 

 structure in the case of this very successful resolution with a xiry 

 objective (N.A. — 1); and it is important to observe that it will 

 only just reveal it. Now to see scale divisions well we do not place 

 the scale so that they are only just separable. Even double the 

 angular limit is advisable — and in some cases more. We may safely 

 then take more like 1,000 magnifications for N.A. — 1, and up 

 to 1,500 for N.A. = 1.5. This is precisely one of those data that 

 cannot be definitely stated. We may, in fact, use 10 times the 

 above minimum magnification in certain cases with advantage. But 

 attention must be paid to one consideration in regard to which the 

 graduated scale analogy is misleading. We bring a scale nearer 

 not only to see the graduations easily, but to estimate small fractions 

 of a division correctly. This presupposes that the marks are very 

 fine — much finer than the interval between them. Now, in the 

 image of an object whose structure is comparable with e — X/2 

 there may be detail, but this detail is quite unlike the object. The 

 artificial detail may be made clearer by extra magnification; but 

 if the purpose of the observer is to find what the object is like^ 

 and not that of an investigator of the errors of optical images, the 

 revelation of this artificial detail is useless and misleading. The 

 only justification for excessive enlargement is when the image is 

 thrown on a screen for inspection by a class, or similarly when 

 a photographic print is made for the same purpose. In these cases 

 it is intended to be observed from a distance; and the useful mag- 

 nification is then such as will enable the true detail to be seen 

 while the finer false detail will be blurred and inconspicuous. We 

 must, therefore, distinguish between useful and useless magnifica- 

 tion. It ought to be observed that it does not matter so far as 

 this question is concerned whether the magnification is chiefly or 

 entirely due to the objective. The eye-piece may be disp\ensed with, 

 as is sometimes done in photomicrography; the calculation will not 

 need any change. 



This question should also be looked at from another standpoint. 

 The eye-piece forms an image of the back lens of the objective- 

 outside itself; this is the " bright spot," or Ramsden circle. The 

 rays that go through the bright spot are all those which penetrate 

 the objective and a.re not stopped. The diameter of this spot i^ 



approximately - x diam. of back lens of objective, where T is 



the tube length and f the focal length of the eye-piece. Now irt 

 telescopes this can be larger than that of the normal eye-pupil with 

 low powers, and in such a case only a part of the diameter of the- 

 object-glass is used. This can only happen with very low powers 

 in microscopy. But with high powers (f small) the bright spot 

 is very small, so that only a part of the pupil is effective. Now 

 Helmholtz concluded that the normal eye-pupil will not bear much 

 reduction without the image seen deteriorating, owing to imperfec- 

 tions in the eye. This point is not easy to demonstrate, because reduc- 

 tion in the aperture of the eye at first improves definition, since the 

 eye is by no means free from aberrations. In my own case a fine 

 line begins to be impaired when the pupil is limited to 2 mm. dia- 

 meter by an artificial diaphragm. The decrease in sharpness 



