INTERPRETATION OF THE N.A. TABLE 435 



n 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 ouli/ n-ill be brougld 

 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 onl;/ 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 emitting 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' 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 

 appeal- 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 interpretation of 

 structure. 



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

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



F F 2 



