370 
SUMMARY OF CURRENT RESEARCHES RELATING TO 
simple grating. The angle a of divergence of the maxima of the second 
order is given by the equation 
X 
sin a = -■> 
e 
X being the wave-length of the light, and e the linear separation of the 
elements of the structure considered. 
In order to show the role of the wave-length in these phenomena of 
diffraction, the author examines a valve of Pleurosigma angulatum with 
a dry objective with aperture a = 0*90, while projecting successively 
on the mirror of the Microscope the different parts of a spectrum. 
If u denote the 1/2 angle of aperture of the objective, in order that 
the Microscope may give us an image of a structure composed of 
elements of which the linear separation is e, we must have for the axial 
illumination 
X 
sin u = -» 
e 
and since the numerical aperture a = n sin u where n is the index of re- 
fraction of the medium between the objective and the object, 
X 
a = n sin u = - • 
e 
For illumination at its maximum of obliquity 
X 
a = n sin u = — > 
2e 
whence 
X 
which is the formula of Helmholtz and Abbe. The resolving power 
thus depends not on the magnification, but only on the wave-length and 
the aperture of the objective. 
The extreme limits of wave-length which we can utilise in the actual 
conditions are X = O’ 40 p, for direct observation and X = O’ 35 /x for 
photography. The angle of aperture of the objective cannot exceed 
140°-160°, and the highest numerical aperture is 1*6. In these con- 
ditions the Microscope can show us elements of structure distant 0 • 17 /x 
from each other, i. e. 5800 elements to the millimetre, with white light. 
With violet light X = 0*44 /x of the spectrum we reach to e = 0*14 /x, 
with 7000 elements to the millimetre ; with photography X = 0 # 35 /x, 
e = 0 # 10, i. e. 10,000 elements to the millimetre. 
For the resolution of molecules, if we take for the dimension of the 
molecule 1/1000,000 mm., i.e. e = 0*001 /x, we should require apertures 
equal to 175 to 220 or wave-lengths of 0*005 /x. This shows clearly 
that the vision or photography of molecules by means of the Microscope 
is a thing pliys’cally impossible. 
