INTERPRETATION OF THE N.A. TABLE 



435 



si square grating having 25,000 holes per linear inch at the focus of an 

 objective at P, P D the dioptric beam, P 1 P 1 diffraction spectra of the 

 first order, and P 2 P 2 those of the second order, then if the objective 

 is aplanatic all those spectra will be brought to an identical focal 

 conjugate ; and the image of the grating will be a counterpart of the 

 structure, characteristic of such a group of spectra. Let us suppose 

 our objective to be over-corrected, as in fig. 369, then when the grat- 

 ing is focussed at P the spectra of the first order only will be brought 

 to the focal conjugate ; the image, however, will not be materially 

 affected on that account, as the diffraction elements of the first order 

 are alone sufficient to give a truthful representation of the 25,000 

 per inch grating. If, however^the objective be raised so that the 

 grating lies at P', the, diffraction' elements of the second order only are 

 brought to the focal conjugate; consequently by the hypothesis the 

 image will have 50,000 holes per linear inch, or double that of the- 

 original. In other words, placing a grating at the longer focus of an 

 over-corrected objective is apparently tantamount to cutting out the 

 diffraction spectra of the first order by a stop at the back of the 

 objective. 



The effect of this is to give an impression that there is a strong 

 grating with 25,000 holes per linear inch ; and over it another grat- 

 ing with 50,000 holes per linear inch. The raising the focus so as 

 to bring P to P 7 necessarily gives the idea of the fine structure being 

 superimposed on the coarse. Therefore the microscopist should 

 beware, whenever he notices a structure of double fineness over 

 another one, lest he has a condition of things similar to fig. 369, The 

 following is a test which may be applied to confirm the genuineness of 

 any such structure. First measure by means of the divided head 

 of the fine-adjustment screw, as accurately as possible, the 

 movement required to bring P to P' in fig. 369 ; next by means 

 of the draw- tube increase the distance between the eye-piece and the 

 objective : this will have the effect of increasing the over-correction 

 of the objective, and a state of things will be obtained as in fig. 370. 

 Hence it will require a larger movement of the fine-adjustment 

 screw to bring P to P'. This will make the distance between the 

 50,000 grating and the 25,000 grating appear greater than it was 

 before. If this takes place the 50,000 grating is a mere diffraction 

 ghost. It is well to note that we have seen a photograph by 

 Mr. Comber of a diatom surface which is uneven. In those parts 

 where the focus is correct the structure is single, but in the parts 

 where the focus is withdrawn it is double. 



A precisely similar condition of things exists with an under- 

 corrected objective, only in that case the false finer grating will 

 appear below the original coarse grating, and to increase the distance 

 between them the draw-tube must be shortened. 



It may therefore be of service to give an example of the use of 

 the numerical aperture table as a check in the inter pretation of 

 structure. 



Fig. 371 gives six illustrations of the back of an objective (the 

 eye-piece being removed) of -83 X.A., or 112 in air. D stands for 



F F 2 



