Flat-Wavelet Resolution, 581 



with the mathematical results obtained from the differential 

 equation. 



30. Accordingly, in dealing with the media we meet with 

 in making experiments we must contrive such a succession 

 of imagined events as will justify us in conceiving the actual 

 medium (which may be air, or glass, or oil, or any of the 

 media in which microscopical objects are mounted) replaced 

 by a medium fulfilling the foregoing conditions. This can 

 be accomplished in perfection by employing the methods of 

 investigation placed within our reach by the Principle of 

 Ixeversal. This has been done in the first paper of the present 

 series, that published in the Eeport of the British Association 

 for 1901, so far as concerns resolution into flat wavelets; and 

 the slight modification of the proof to make it available for 

 resolutions into convex or concave wavelets is given in the 

 Appendix to the present paper. 



In these proofs the space within which the resolution is 

 effected is any space lying within the sphere r mentioned in 

 those papers, where we are at liberty to assign any length 

 we please to r, the radius of this sphere (see the diagram on 

 p. 596). 



31. To give definiteness to our research we shall fix upon 

 a definite instance, selecting one which we shall find useful. 

 We shall make it our definite aim to resolve into its plane 

 wavelet components the light which crosses the air space that 

 intervenes between the cover-glass protecting a microscopical 

 object and the front lens cf the objective (here assumed to be a 

 " dry " objective) when the microscope is focussed upon the 

 object. The light that crosses this air space has come either 

 wholly or partly from the microscopical object. It may also 

 partly have come from surrounding unoccupied portions of the 

 field of view. We shall use the phrase microscopical objects, in 

 the plural, to imply the whole contents of this field. It will 

 facilitate our descriptions to suppose the microscope pointed 

 directly downwards, in which case the air space spoken of 

 above will be a horizontal stratum of air which vve may call 

 stratum S. We shall also picture this stratum as not of 

 limited extent, but as extending indefinitely between two 

 bounding planes — the horizontal plane in which the front 

 face of the front lens of the objective lies, and the parallel 

 plane in which the upper surface of tin; cover-glass lies. It 

 i- the resolution into u f \v\s of tin; light within this air space 

 as it travels upwards, that can be exhibited experimentally in 

 the microscope, as will be explained further on. We shall 

 find it convenient to make the same supposition of unlimited 

 extension sideways, in the ease both of the cover-glass and 



