574 REPORT— 1901. 



Theorem V. 



The light of wave length X which reaches the image of an object formed by 

 an optical instrument may be resolved into undulations of uniform plane wave- 

 lets, of which only one undulation need be provided for each of the directions 

 along which light reaches the image. 



This theorem is a particular case of Theorem IV. 



Light may be resolved into wavelets in innumerable ways. Amongst these 

 the analysis into undulations of uniform plane wavelets possesses the unique 

 advantage that as each undulation advances through space neither it nor any of 

 its 2}arts undergoes change. Hence 



Theoeem VI. 



To estimate the effect produced within a closed space or by the light that has 

 reached a given image, it will suffice to draw cylinders enveloping this space or 

 image, in all the directions from which light comes to it, and to confine our 

 attention to the portion of each undulation of uniform plane wavelets which lies 

 within that one of the cylinders which is perpendicular to its wave fronts. 



From this group of theorems others of much interest follow ; but to describe 

 the method by which they are derived would necessitate entering upon new ground,, 

 and would unduly prolong the present abstract. It must therefore suffice to say 

 that by some of these further propositions a beam or pencil of light is resolved into 

 its plane-wavelet components, each of indefinite extent laterally ; and that this; 

 resolution renders possible a study of the phenomena of diffraction gratings when 

 the portions of liglit that reacli the individual reflecting strips come from inde- 

 pendent sources. 



Some of the Results Obtained. 



These theorems have made it possible to investigate the distribution of the light 

 which is thrown ofl' by visible objects, and they explain the experimental effects 

 seen by Professor Abbe when light was incident upon microscopical objects under 

 various limitations as to direction. In the covirse of the inquiry the total light 

 incident on an object, or else the total light which emerges from it, has to be 

 resolved into its plane-wavelet components ; and it appears on applying tliis 

 method of analysis, either to the incident or to the emergent light, that the por- 

 tions of light thrown oft' by different parts of the object are capable of interfering, 

 whether those portions of light had reached the object from tlie same or from 

 independent sources. 



Verification by Experiment. 



After confirming these results by a repetition of Abbe's observations and by a 

 large range of other experiments (vith the microscope, it appeared to the writer to 

 be desirable to contrive a test experiment which could be carried out with more 

 precision than is possible when employing the microscope. 



A ruling of parallel equidistant lines seems from the theoretical point of view 

 to be the simplest kind of visible object with detail upon it to be seen. Accord- 

 ingly the object chosen for experiment was a Rowland's diffraction grating with 

 a ruling a little more than 4^ centimetres long, and containing about 26,000 

 reflecting strips. 



The theoretical investigation indicated that the light thrown off by the grating 

 should be in the same directions and have the same intensities, whether the 

 incident light which has reached the several reflecting strips have come from the 

 same or from difl'erent sources, provided that, if they come from different sources, 

 equal intensity of light has reached the several strips. 



To test this Miss E. A. Stoney proposed to bring light from independent sources 

 to the various parts qf the grating by throwing an image of the sun upon it ; 



