Application of Undulatory Theory. By A. E. Conrady. 403 



one another, and then their relations to each other will change 

 with such lightning-like rapidity that the human eye cannot 

 realise these relations separately, but receives only an average 

 impression. 



It becomes at once apparent that light from two independent 

 points cannot have any permanent relationship when we consider 

 that two such points may, and probably will, at any one instant 

 be sending out light of different wave-length, which latter more- 

 over is subject to gradual change in either point, and further, that, 

 if we imagine ourselves looking towards any such point, the trans- 

 verse vibrations may be taking place in any direction whatever 

 across the line of sight, thus opening another source of great and 

 changeable differences between the light from such independent 

 luminous points. The common experience is therefore that we 

 cannot obtain interference phenomena when light from different 

 sources is intermingled ; each source contributes its own share to 

 the total brightness of the illumination, the latter being simply 

 the sum of the individual intensities. 



No formula which contains a phase-relation and which deals 

 with amplitudes can therefore apply to the combination of undula- 

 tions which have originated in independent sources of light, and to 

 assign such a formula to such a purpose would clearly prove a 

 complete unaccpuaintance with the elementary principles of physical 

 optics. 



The case of the combined effect of light from a number of 

 different independent sources is thus settled, and nothing that 

 follows must, or can, be applied to such a case ; and as interference- 

 phenomena thus become limited to cases where light from the 

 same source reaches a certain point by paths of different lengths, 

 we see that it is the study of the resultant brightness in such cases 

 that must provide the solution of the problems of the action and 

 resolving power of optical instruments. 



Any luminous particle sends out spherical waves, and as these 

 are the result of the vibration of the particle, we see at once that 

 the light must at any given time and distance be performing the 

 same kind of vibrations within a wide angular extent, and that for 

 tins reason light from a distant point must be capable of inter- 

 ference even though the portions brought together formed widely 

 separated parts of a wave. This is indeed borne out by the ex- 

 perience with large telescope object-glasses, for in these it is found 

 that the light from a distant star passing the different zones pro- 

 duces diffraction-phenomena precisely similar to those obtained 

 with small apertures. A more difficult question is the one as to 

 how great the difference of phase may become before the gradual 

 changes in the rate and direction of the vibrations become manifest 

 and prevent regular interferences. All we can say is that experi- 

 ence with large diffraction gratings and still more with interfero- 



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