Flat- Wavelet Resolution. 585 



the light which reaches the objective as being light which 

 was emitted by the several puncta of image G, and as having 

 come from them direct through air (or oil) to the front lens 

 of the objective. 



37. Hitherto we have for the most part dealt only with the 

 ca>e where the medium between the cover-glass and the 

 objective is air. If the objective we are using is an oil- 

 immersion objective, the procedure will be essentially the 

 same : only we have now to substitute theoretically trans- 

 parent oil for real oil, to imagine space K filled with an 

 extension of this oil, and to suppose the standard images B 

 and C to be formed in a continuation downwards of the same 

 medium. 



38. We shall freely make use of the conception presented 

 above, that the light coming to the objective has emanated 

 from the standard image — either B or C. This is a much 

 simpler apparatus than the real apparatus which consists of 

 the microscopical object, with molecular motions and other 

 detail immensely too fine to be reproduced in any real image ; 

 and vet the simpler machinery we have substituted would 

 supply to the objective precisely the same light as that which 

 really reaches it. 



39. Moreover, we may imagine the light emitted by each 

 punctum of the standard image to be resolved into its plane 

 wavelet components ; so that, if X is the number of optical 

 puncta in the standard image there will be N ufw's traversing 

 space S in each upward direction. The number of these 

 however may be greatly reduced. Those of them travelling in 

 any one direction may be combined into a single resultant 

 u f w advancing in that direction; so that finally the whole of 

 the light in space S is resolved into uf w's of which one only 

 needs to he provided for each upward direction. It is the 

 resolution of the light when it attains this final form, that 



shall find it possible to exhibit experimentally in the 

 microscope. 



40. To do so, we have to trace the further progress of these 

 resultant u f w's. Those of them whose guide lines — lines 

 perpendicular to the planes of the waves — are not too much 

 inclined to the optic axis of the microscope will, parts of them, 

 not onlv enter but will be transmitted through, and will each 

 of them be brought to a focus by, the objective. What there- 

 upon happens may be strikingly illustrated by a very simple 

 experiment. Look towards some distant landscape, and hold 

 one of the objectives of the micro-cope at a distance of about 

 ten inches from the eye, with it> front lens towards the land- 



■ and its buck lens towards the observer. An inverted 

 Phil. Mag. 8. 6. Vol. !'. No. 52. April 1905. 2 Q 



