84? Mr. R. Potter on a -particular Modification 



with nature, and for which they have offered but very unsatis- 

 factory arguments, I must claim as strongly in favour of the 

 view which I have proposed. There are, indeed, cases in which 

 the undulatory theory affords a direct application, as in the 

 transmitted colours of thin plates, and in the fringes within the 

 shadows of narrow bodies : but on a careful review we must 

 allow that these cases arise in less simple circumstances than 

 those exceedingly numerous ones in which the claim of half an 

 undulation has to be made. 



Having shown how interference may arise according to the 

 theory that light is caused by an emitted matter, I shall pro- 

 ceed to the mathematical investigation of the experiment with 

 the prism, which has been before described. 



To find the central points of interference after the refrac- 

 tion of the pencils by the prism, requires the previous conside- 

 ration of three distinct questions ; namely, 1st, The positions 

 of the secondary images of the luminous point, or the centres 

 of divergence of the rays after the two refractions : 2nd, The 

 simultaneous positions of the luminiferous surfaces : 3rd, The 

 figure of the curve of the principal section of these surfaces ; 

 — the plane of this section being common to both pencils. 



The first question involves only the common rules of optics; 

 the other two require, in addition, the application of the re- 

 spective theories as to the velocity with which the light passes 

 through the substance of the prism. 



From the properties of the prism we cannot rigorously 

 consider the light which emanates from a luminous point 

 before refraction to do so afterwards, excepting for very small 

 pencils near the angle of minimum deviation ; for which rea- 

 son I shall only investigate the principal part of the problem 

 on this supposition, of exceedingly small pencils, incident on 

 the prism near the angle of minimum deviation. I do not 

 nevertheless consider that it would lead to objectionable re- 

 sults for other incidences : in making the corresponding ex- 

 periments, however, some care would be requisite to be taken, 

 to preserve the direction of the bands perfectly parallel to the 

 line bounding the angle of the prism. We find that inter- 

 ference, according to the rules, is not prevented by even the 

 great degree of aberration which exists in the focus of the lens 

 we use to form an image of the sun, and which, though of 

 considerable dimension, we consider in calculation as a lumi- 

 nous point. The effect of these imperfections generally tends 

 to render the phenomena less distinct and less sharply ex- 

 hibited; or, where it was required to determine whether the 

 central band were a bright or a dark one, this aberration would 

 present a serious obstacle. 



