18 MORPHOLOGY 



different ways. P^ach of them is subject to the limitations imposed by the optical 

 system employed. 



Stained or unstained preparations may be examined under the microscope, using light 

 transmitted through a sub-stage condenser of the ordinary type. The hmit of resolution, d, 

 (that is, the shortest distance by which two particles must be separated in order that they 

 may give distinct images) is determined by the wave-length of the light and the numerical 

 aperture of the objective. It is given by the formula, 



Q-5A 



where X = wave-length of hght used, and N.A. = numerical aperture of objective. 



The possible range of A is obviously Umited to that part of the spectrum to which the 

 human retina is sensitive, and the numerical aperture is subject to the technical hmitations 

 of the optical system employed. In practice, the highest N.A. that can be employed with 

 transmitted Ught is about 1-4, and this, when used with monochromatic hght with a wave- 

 length of 546 m/i, corresponding to the green mercury line, gives a resolving power of 



546 1 



-^ X r-^ = 195m^ = 0-2// (approximately) 



This degree of resolution is obtained only under optimal conditions, and in ordinary practice 

 the hmits of resolution are reached with particles that have a diameter of about 0-25 /i. 

 Merling-Eisenberg (1937) has modified the formula by introducing a factor measuring 

 the intensity of illumination. By suitably reducing this intensity a limit of resolution 

 of 0-08 ft is approached. Under ordinary conditions, however, objects smaller than 0-25 /ii, 

 though " seen " in the sense of being visible, do not form images that reveal the real size 

 or shape of the particle. 



Another method is that known as dark-ground Ulumination. The bacteria, or particles, 

 are examined unstained, and the light passing through the special sub-stage condenser is 

 directed along a path such that only those rays that are refracted, diffracted, or scattered 

 by the object under examination reach the eye of the observer. Bacteria so examined 

 appear as bright images on a dark background. This method is vastly superior to the 

 former as a means of examining Uving, unstained organisms, but it is subject to the same 

 limitations in regard to resolution ; and, since the highest N.A. at present available for 

 use with Ulumination of this type is about 1-27, the smallest particle that can be resolved 

 has a diameter of about 0-35 fi. 



The third method, which has been developed particularly by Barnard (1919, 1925, 

 1930), extends the hmits of resolution by decreasing the wave-length of the light used. 

 Usmg ultra-violet hght with a wave-length of 257 m/n and an optical system of quartz 

 lenses, Barnard has been able to photograph and resolve particles with a diameter of 

 0-075 fi. Beyond this point a hmit is again reached, due to the lack of a refracting 

 material that wUl transmit light of shorter wave-length. The degree of mternal structure 

 that may be revealed in certain bacteria by ultra-violet photography, combined with dark- 

 ground illumination, is illustrated in Fig. 4, for which we are indebted to Mr. Barnard. 



The electron microscope devised by Ruska (1934) and by Marton (1934) provides 

 the fourth method of examination (see Marton 1941). The fact that an electron beam 

 passing through a magnetic field behaves in a manner closely analogous to a beam of 

 light passing through a refractmg medium permits the construction of a microscope 

 generaUy similar to an optical microscope, and its description in the terminology of hght 

 optics. The " lenses " are circular electro-magnets whose focus varies as the strength 

 of the applied magnetic field ; and the microscope has a " condenser " coU, an " objective " 

 coil, and a " projective " coil, the last being equivalent to the eyepiece. The " wave- 

 length" is a function of the speed of the electrons, and those used in electron microscopy 

 are equivalent to a wave-length about l/100,000th that of visible hght. Resolving powers 

 commensurable with this wave-length cannot be attained in practice, since " chromatic " 

 aberration in the magnetic lens cannot be corrected, and " spherical " aberration is over 



