4 Transactions of the Society ' 



point, which it should be remembered is often brought home to 

 the worker with the microscope, more often perhaps than any other, 

 was first determined theoretically, and afterwards was proved in 

 practice to be well-founded. The method of practical proof was by 

 means of a Grayson ruling. By a fortunate chance two of these 

 lines in the latter projected beyond the rest, so that a pair of objects 

 of known distance apart could be observed. By gradually reducing 

 the numerical aperture of the observing objective, it was shown tliat 

 the projecting parts of the lines could be seen as two separate 

 objects after the remaining rulings were ubliterated, and 

 that they appeared to be farther apart than the distance between 

 the rulings. As you are aware, the theory enunciated by Abbe, 

 and known as the diffraction theory, takes a grating as a typical 

 object. From this we know that the two factors determining the 

 limits of resolving power are the numerical aperture of the objective 

 and the mean wave-length of the light used. Under the most 

 favourable circumstances then the practical limit is reached when 

 objects in a row are about '20^11 apart, or a pair of objects can be 

 differentiated when they are about five-sixths the distance apart of 

 those that can be separated, if they are in a regularly recurring 

 series. 



These limits of resolution for two separate objects may also 

 be taken as the absolute limit of resolution for an isolated object 

 that can be seen and observed as a definite entity. It represents, 

 in fact, the smallest object we can see as a dark body on a bright 

 ground, while being able to ascertain its definite form ; but it does 

 not by any means represent the limit of visibility. This point is 

 essentially different, and brings us to a consideration of bodies 

 which can be observed as self-luminous ones on a dark background. 

 The method is well known enough, and when it involves the 

 observation of objects which are well within the resolution limits 

 is referred to as dark-ground illumination. When an object is 

 rendered visible which is small in all dimensions in comparison 

 with a wave-length of light, the object is said to be ultra- 

 microscopic. Lord Eayleigh has shown that the limits of visibility 

 are dependent on the difference of refractive index between the 

 object and the medium in which it lies, and on the intensity of 

 the illumination. Under conditions which result in the object 

 becoming a self-luminous one, it is therefore difficult to assign 

 a definite limit to visibility. In the case of metals like gold 

 and silver in the colloidal state, in which the refractive . index 

 differs greatly from that of water, the medium in which they may 

 be immersed, the limit of visibility depends on the amount of 

 light that can be concentrated on such particles and on their 

 separation. On the other hand, in the case of certain organic 

 colloids, such as albumen, the particles are not easily made visible, 

 because of the small difference of refraction existing between them 



