19.2 M. F. Eisenlohr on the Vibration of Light. 



het we have PN = — — ^. Meanwhile a circular wave will 



have spread from the point M, and in the time t will have 

 acquired a radius tw; but at the same time it will have been 

 carried back a distance ct, so that its centre, instead of being 

 at M, will be at W, a distance cf within the prism (it being 

 of course understood that the wave which has issued from the 

 prism remains outside). The position of the emerging ray 

 is therefore obtained by drawing from N a perpendicular upon 

 the line ]\I'R = ^«'. In order to observe this ray, however, the 

 telescope must be brought into the position ME, ; because if MR 

 be its length, the fether moves from M to M' in the same time 

 that it takes a ray moving in fether at rest to pass over the di- 

 stance ]\I'R, so that the ray takes the resultant direction MR. 



Now the experiments of Arago have shown that this direction 

 is identical with that which the refracted ray would have in still 

 ffither ; at least so far as the accuracy of the expermients went, 



which took account of the ratio A but not of its square. This 



fact may be used to determine A ; for if, from N, the perpendicular 

 NS be let fall on MR, then, from what precedes, we must have 

 MS = nV'^ = tw-ct^. Drawing, then, MU perpendicular to 



BC and UV perpendicular to MR, on account of the similanty 

 of triangles RNS and URV, and of triangles NMS and MUV, 



we have ,,„ 



NS . UV= RS . RV=MV . MS ; 



and from the last equation it follows, as may easily be seen, that 



n 



MS = RV = ^w-c/-^, 



whence , „,, 



n_^w-RV_M 'R-RV 



a:~ ^t MM' • 



On account of the smallness of the angle M'RM UR = VR 

 nearly, and therefore M'R-RV = M'U ; and if TM' be drawn 

 parallel to UM, TM may be substituted for UM', from which it 

 differs inappreciably, and we get 



n _ MT sinMM'T 

 A'MWsinMTM" 



in which only those magnitudes are neglected which depend on 



the square of -, and which therefore elude observation. 



