The London, Edinburgh and Dublin philosophical magazine and journal of science . projection is usuallyexhibited on some parallel plane. The positions of the index-points—/. e. o£ the projections o£ the guide-points—are thesame in the resultino- diagram, whether it is formed on thebase-plane or on any parallel plane. 10. Accordingly, if uu u2, &c. are the u f ws we have todeal with, then the directions in which they are advancingand the orientations of their wave-fronts, are adequatelyrepresented by the index-points Il5 I2, &c. got by the aboveconstruction ; and whether the projection by which
The London, Edinburgh and Dublin philosophical magazine and journal of science . projection is usuallyexhibited on some parallel plane. The positions of the index-points—/. e. o£ the projections o£ the guide-points—are thesame in the resultino- diagram, whether it is formed on thebase-plane or on any parallel plane. 10. Accordingly, if uu u2, &c. are the u f ws we have todeal with, then the directions in which they are advancingand the orientations of their wave-fronts, are adequatelyrepresented by the index-points Il5 I2, &c. got by the aboveconstruction ; and whether the projection by which we arriveat the index-points is a projection on to the base-plane or onto some parallel plane, they occupy the same positions withina circle in that plane which is the projection upon it of theflat side of the reference-hemisphere, and which, therefore,has R for its radius. This circle and its contents may becalled the Indicator-diagram. 11. By applying simple geometrical considerations to theforegoing construction, we get the following propositions :— Fig- Indicator-diagram. Let Ui and u2 be two in ward-bound u f ws, consisting ofwaves similarly polarized and of wave-length X : and let I1and I2 be their index-points upon the a simple geometrical proof furnishes the followingelegant theorem. ©v Theorem VII * The light which these two ufws throio » the base-plane,or on any parallel plane, is a luminous riding perpendicular * The propositions in this paper are numbered in succession to thosein the paper at p. 570 of the B. A. Report for L901. 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 ifwe know the position of any one of the points which the twoundulations reach simultaneously in the same phase. Weshall use the letter k to designate such a point. 12. Hitherto we have considered only individual u f us now
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