270 Dr. G-. J. Stoney on the Resolution of Light 



to the line d ; and the spacing from crest to crest of this ruling 



" ■ B 



The position of this ruling will become fully determined if 

 we know the position of any one of the points which the two 

 undulations reach simultaneously in the same phase. We 

 shall use the letter k to designate such a point. 



12. Hitherto we have considered only individual u f w t 's. 

 Let us now consider an entire sheaf of them. By a sheaf oi 

 u f w's is meant a group of them whose guide-radii form a 

 solid cone. It will be represented either by this cone, which 

 may be called the guide-cone of these undulations, or by their 

 guide-patch (in which this cone intersects the surface of the 

 hemisphere) ; or preferably by the projection of this guide- 

 patch upon the indicator-diagram, which we may call the 

 macula of the sheaf of u f w's. 



Thus a point on the indicator-diagram represents a single 

 u f w, a macula (or patch on the indicator-diagram) represents 

 a certain sheaf of such undulations. 



Let it further be provisionally assumed that the undulations 

 of this sheaf all reach the point k in identical phases at each 

 instant of time, that they are polarized alike, and that they 

 have equal intensities. The point k, which the undulations 

 of the sheaf reach in identical phases, may be either on or off 

 the base-plane. Draw through k a plane parallel to the base- 

 plane, and call it plane K\ or it may be called the screen K, 

 as we are about to inquire in what way it is illuminated by 

 the light with which we are dealing. 



13. The macula of the sheaf may have any shape or size. 

 Let us begin with the simple case where the sheaf of undu- 

 lations is such that its macula on the indicator-diagram is a 

 rectangle with sides a and b. Bisect ^. 



this macula, as in the figure, by a line D * ' 



parallel to one of its sides, and let l x . , 



and 1/ be similarly situated points in „ I c 



the two halves. The line connecting a , Z^ \ J' 



them is parallel to 6, and = b/2. Hence, 



by Theorem VII., the two u f w's of 



i • i x it/ j/l • j • j. A rectangular macula ou 



which I, and Ij are the mdex-pomts the Indi J at01 .. di 



would, it they alone were present, 



produce on plane K a luminous ruling of which one crest 



passes through k, of which the crests are perpendicular to 



the line b of fig. 3. and which are spaced asunder by the 



interval ^ 



<7 = \—. J-. 

 



