Presidential Address. 3 



thickness varying from 1 micro-millimetre up to 360 micro- 

 millimetres. The three black bars on the extreme right represent 

 on the same scale the resolving power of the three microscope 

 objectives with which we are, perhaps, most familiar, and which 

 are to be found in most batteries of objectives that are used for 

 accurate work. The numbers at the lower ends of the bars are the 

 numerical apertures of these lenses. 



" Taking the third of the series, which is marked as having 

 a numerical aperture of 1'4, its length is about 150 micro- 

 millimetres. This means that if two lines were ruled on a glass 

 plate, 150 micro-millimetres apart, they would be seen as two 

 distinct lines by means of this lens. With either of the other two 

 lenses the lines would merge into one : the lens would fail to 

 resolve them." 



" The diagram shows at a glance that an object may be visible 

 to the unaided eye, even though one of its dimensions is far below 

 the range of microscopic resolution. For example, the thickness of 

 a gold-leaf is about 90 micro-millimetres — that is to say, it is 

 60 millimetres below the resolving power of a lens of 1*4 N.A. 

 Yet we can see the surface of a leaf with the unaided eye, and can 

 examine it microscopically without difficulty ; but if we try to see 

 the edge of the leaf we shall fail, for instead of the real edge we 

 shall see an ill-defined edge, the apparent width of which would 

 entirely depend on the aperture of the lens used. With a 1 * 4 lens 

 the apparent width will be 150 micro-millimetres; with an 0*65 

 it will be 300 micro-millimetres ; and with an 0*3 it will be 

 700 micro-millimetres. The obvious lesson from this is that in 

 using the microscope in this region of micro-dimensions, we must 

 be careful to keep its limitations, and their possible effect, always 

 in mind." 



In any consideration of the limits of resolving power we have 

 to remember that whenever image-formation by a lens-armed 

 aperture takes place the resulting image of a point is no longer a 

 single point, but a circle of light surrounded by diffraction rings. 

 The result is that in the microscope every optical appliance avail- 

 able must be employed at its best, and optical accuracy of the 

 highest order must be attained to ensure the production of a correct 

 image, one in which these diffraction fringes are least in evidence. 

 If we consider the observation of two objects, or elements in an 

 object, then we shall fail to resolve them if they are so close 

 together that the diffraction image from one overlaps that from the 

 other. The same applies to a grating or series of contiguous points 

 in an object, except that Johnstone Stoney has shown that two 

 points in an object may be somewhat closer together and yet 

 be resolved than the lines of a grating which are of the same 

 distance apart. Also that two such objects would appear to be 

 somewhat farther apart than they actually are. This important 



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