THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FIFTH SERIES.] 



JUNE 1890. 







LI. The Theory of Fog-Bows. By James C. M c Connel, 

 M.A., Fellow of Clare College, Cambridge*. 



[Plate X.] 



THE supernumerary bows often seen within the ordinary 

 rainbow received their first explanation, bordering on 

 the truth, from Thomas Young f. In the principal plane 

 through the centre of the drop, as we increase the angle of 

 incidence from zero to a right angle, the deviation of the rays 

 from their original direction at first diminishes, gradually 

 reaches a minimum, and finally increases again. So for any 

 deviation slightly greater than the minimum there are two 

 emergent rays which have travelled paths of slightly different 

 length and are in a condition to interfere. By the interference 

 of such Young supposed the supernumerary bows to be formed. 

 Now the wave theory in its essence knows no such thing 

 as rays, and they should be regarded merely as convenient 

 symbols for obtaining approximate results when the wave- 

 surfaces are spherical. In all ordinary cases the wave-surfaces 

 may be treated as spherical, but the rainbow is an exception. 

 The wave-surface of the emergent light changes the sign of 

 its curvature at a point corresponding to the ray of minimum 

 deviation ; and thus we have diffraction phenomena, depend- 

 ing merely on the peculiar shape of the wave- surface, without 

 any limitation by screens. 



* Communicated by the Author. 



f Phil. Trans. 1804 ; or Encyc. Brit., eighth edition, art. " Chromatics.' 



Phil Mag. S. 5. Vol. 29. No. 181. June 1890. 2 N 



