132 Astronomical and Nautical Collections, 



and QB = SQ. The points A and B, thus found, are the 

 centres of divergence of the rays reflected from the respective 

 mirrors, according to the well known law of reflection. 

 Thus, in order to have the direction of the ray reflected at 

 any point G of the mirror DF, for example, it is sufficient 

 to draw a right line through B and G, which will be the 

 direction of the reflected ray. Now it must be remarked, 

 that, according to the construction by which the position of 

 B is found, the distances BG and SG will be equal, and 

 thus the whole route of the ray coming from S and arriving 

 at b, is the same as if it had come from B. This geometrical 

 truth being equally applicable to all the rays reflected by 

 the same mirror, it is obvious that they will arrive at the 

 same instant at all the points of the circumference n'bm, de- 

 scribed on the point B as a centre, with a radius equal to 

 Bb ; consequently this surface will represent the surface of 

 the reflected undulation when it arrives at b, or, more cor- 

 rectly speaking, its intersection with the plane of the figure : 

 the surface of the undulation being understood as relating to 

 the points which are similarly agitated at the same instant : 

 the points being all, at the commencement of the whole oscil- 

 lation, for example, or at the middle or the end, completely 

 at rest ; and in the middle of each .semioscillation, possessed 

 of the maximum of velocity. 



In order to represent the two systems of reflected undu- 

 lations, there are drawn, with the points A and B for their 

 centres, two diff'erent series of equidistant arcs, separated from 

 each ether by an interval which is supposed equal to the length 

 of a semiundulation. In order to distinguish the motions in 

 opposite directions, the arcs on which the motions of the ethe- 

 real particles are supposed to be direct, are represented by full 

 lines, and the maximum of the retrograde motions are indi- 

 cated by dotted lines. It follows that the intersections of the 

 dotted lines with the full lines are points of complete dis- 

 cordance, and of course show the middle of the dark stripes ; 

 and, on the contrary, the intersections of similar arcs show the 

 points of perfect agreement, or the middle of the bright 

 stripes. The intersections of the arcs of the same kind are 

 joined by the dotted lines by, br, b'p, and those of arcs of 



