452 ON" APEilTFKE AND DEFrKrillON OF MICEOSCOPE OBJECT GLASS. 



capacity, of which ''aperture" may be considered in a certain 

 sense the measure, we have learnt from Helmholtz and Abbe that 

 the deterioration of image, caused by diffraction effects upon the eye 

 looking through a minute optical aperture at a highly amplified 

 image, is lessened by a relatively larger angle of incident defining 

 pencils, and by other circumstances to be mentioned presently. 

 But the formula of Helmholtz, illustrated in Mr. Sorby's table, 

 shews us how greatly the limits of resolution vary with wave 

 length of colour"^'. The careful study of the optician in producing 

 an '* achromatic " objective is so to equilibriate the extreme red and 

 violet images as to give a colourless image in some intermediate 

 focal plane by counteraction of and compensation for aberrant rays. 

 In remedying these defects of dispersion and deviation, as also in 

 perfecting the amplification needful for resolution of minute objects, 

 the operation of angular aperture is passive only, whilst the 

 co-operation of every dioptric condition on which their correction 

 depends, must be active. Hence, therefore, the dictum that 

 " defining power varies with chord (!) of aperture," besides leaving 

 everything to be explained, is a most incorrect summary of facts. 



"When it is considered that the microscope image is literally 

 delineated in points of light from innumerable pencils, each one of 

 which must touch the focal plane at its proper relative distance from 

 the axis around which the image is formedf, it is manifest that 



* And also how greatly chromatic dispersion interferes with clearness 

 of resolution. 



t The translation of the fundamental law, formularized by Professor Abbe 

 (see page 211 of this vol.), together with the sentence preceding it, having 

 been incorrectly priuted from the MSS., we repeat it here as corrected. " The 

 study of these aperture images leads to various conclusions, the full 

 development of which depends on a priaciple capable of general demonstra- 

 tion, and which may be formularized as a law apphcable to every part of the 

 theory of the microscope in the terms following " : — 



' ' When a sijstem of lenses is perfectly aplanatic for one of its focal planes^ 

 every ray proceeding from that focus strikes the plane of its conjugate focus at 

 some point whose linear distance from the axis is equal to the product of the 

 equivalent focal leyigth of the system and the sine of the angle which that ray 

 forms with the axis." 



On this law of focussing function depends the geometrical dehneation of 

 the microscope image, whose amplification is Hkewise herein indicated as 

 dependiug on focal length and angular aperture of a lens system. 



