ON LIGHT. 371 



and intersecting it in its line of direction. And first, for 

 simplicity, let us suppose the two vibrations of equal in- 

 tensity {i.e.j in both which the molecular excursions on 

 either side of the point of rest are equal), and that their 

 directions form a riglit angle with each other. Let a b 

 and a b, fig. 15, represent two such lines of vibratory 

 movement, c, c, their central points, or the positions of 

 rest of the molecules when undisturbed, and c a, c b ; 

 c a, cb ; their extreme excursions to and fro. The times 

 of vibration being equal (which is an indispensable 

 condition for the union into one of two distinct luminous 

 rays : as a red ray, for instance, cannot interfere with a 

 violet one), let each be supposed divided into the same 

 number of equal parts (say 360). Then supposing the 

 molecules to set out at the same instant from c and c, 

 they will arrive at a a, respectively in 90 such units of 

 time, will have returned again to c c, in 180; have 

 reached b, /;, in 270, and again returned to c and <r, in 

 360. In so doing, however, their motions are not uni- 

 form, but most rapid when traversing the central points, 

 and gradually retarded as they recede from these : so 

 that in equal intervals of time the spaces traversed along 

 the lines C a, c a, will be unequal. Then let the whole 

 time (90) of describing c a, be divided into five equal 

 times of 18 each, and suppose that at the encf of 

 the ist, 2d, 3d, 4th, and 5th of these, the molecule has 

 arrived at the points i, 2, 3, 4, 5. It is demonstrable, 

 then, that the several distances C i, C 2, C 3, C 4, C 5, 

 of these points from c will be to each other in tlie pro- 

 portion of the Sines of 18, 36j 54, 72, and of 90** 



