240 
SUMMARY OF CURRENT RESEARCHES RELATING TO 
limtical analysis based on the properties of luminous waves, and from 
his work there resulted the following principles : — 
(1) When the fineness of a structure, i. e. the interval between two 
elements to be distinguished, is not less than 0*10 //,, everything results 
according to the laws of geometrical optics, and the image is the exact 
representation of the object. If, after having focused in central light, 
the eye-piece be removed, a white circle representing the luminous 
pencil emerging from the objective will be seen on looking into the tube 
of the Microscope. The diameter of this circle varies according to the 
focus and aperture of the objective, and also to the aperture of the 
illuminating pencil. 
(2) If the structure is finer, it produces on the illuminating pencil 
phenomena of diffraction, and on looking into the tube, beside the white 
dioptric pencil a certain number of coloured diffraction pencils will be 
seen, of which the number and the arrangement depend upon the nature 
of the structure examined. These spectra are so much more widely 
separated as the structure which produces them is finer. Thus, in 
the case of Pleurosigma angulatum , with a liigh-power immersion objec- 
tive a central white pencil will be seen with six coloured ones arranged 
regularly round it, and if the latter are blocked out all traces of struc- 
ture disappear from the image. Consequently : 
(3) The diffraction pencils united in the image, alone give the image 
of the structure, and : 
(4) To a given structure corresponds a certain number of diffraction 
pencils, and reciprocally to a given number of these pencils corresponds 
the image of a given structure. But the reciprocity is not absolute, for : 
(5) The admission in the image of all the spectra given by a struc- 
ture is not absolutely necessary fur the formation of an exact image of 
the structure ; but it is possible by the non-admission of a certain number 
of these spectra to either change nothing in the result or to modify it 
altogether, i. e. in other words to give either the image of the structure 
or a different image. 
Thus consider a series of parallel lines at distances apart e. Beside 
the pencil of refraction there will be a double series of spectra to the 
right and left. 
(1) S' 4 S' 3 S' 2 S\ O S 4 S 2 S 3 S 4 . , . 
A structure twice as fine will produce spectra twice as wide apart. 
(2) S' 4 S', O S 2 S 4 . . . 
In all symmetrical structures the admission of one series alone, right 
or left, reproduces the image of the structure. In the case of (1), the 
admission of one only of the uneven spectra reproduces the image ; but 
if by a suitable diaphragm all the uneven spectra are eliminated, and 
only the even or only one of these retained, then an image corresponding 
to structure (2) will be produced. Consequently, by eliminating part of 
the light which reproduces the image of a structure, the image of a 
structure twice as fine and which does not really exist is obtained. 
Accordingly, although the admission of all the spectra is not abso- 
