of Light by Cylinders and Splieres. G75 



interference pattern, and completely accords with the variation 

 of the visibility of the fringes referred to above. 



"When, instead of the cylinder, we have a sphere of glass, 

 these fringes take the form of circles, which were observed 

 with small gla-s beads. In the case of drops of glycerine 

 suspended in turpentine, we have an essentially similar case; 

 and these rings, coloured instead of dark and bright, can be 

 observed even with white light, this latter fact being due to 

 the small difference in the disper.-ions of the two liquids. 



5. Case (b) fx> /j! . 



The case when the cylinder has a slightly higher refractive 

 index than the liquid is interesting on account of the caustics 

 (analogous to the rainbowj fornx d by one or more internal 

 reflexions, appearing in quick succession at very small in- 

 clinations to the direction of' the incident light. For example, 



in a case in which , =1*001 the minimum deviations for 



caustics of the first, second, and third orders are, according 

 to the geometrical theory of Descartes, 8° 50', 14° 31', and 

 19° 52' respective y. And when fju and /n' become more 

 nearly equal, they come still closer together. The, rays which 

 suffer one internal reflexion are here not only in a, position 

 to interfere among themselves, but may actually interfere 

 with rays suffering two or more internal reflexions, so that 

 we should have a set of interference fringes in addition to 

 the usual supernumerary bows. 



The appearance of the fringes actually observed is shown 

 in PI. XX. fig. 2. We have here a system of fringes which 

 begins not in the immediate neighbourhood of the source, 

 but in a direction inclined to that of the incident light — the 

 inclination increasing with the difference between jj, and jx '. 

 Moreover, these fringes are, unlike those in the former case, 

 broad at first, but they rapidly decrease in width with 

 increasing obliquities of observation. Unfortunately, the 

 observations could not be carried further for want of an 

 optically good cylinder, the one available being a very short 

 focus cylindrical lens which, though quite suitable for the 

 case when {J j </jl / , could not be satisfactorily used in the 

 present case with its internal reflexions. 



That the caustics mentioned above arc aetuailx formed 

 could, however, be seen even with an ordinary glass rod 

 immersed in the liquid when the slit was illuminated with 

 white light, more especially when the surface oi the cylinder 

 was examined bv a magnifying lens i ml the direction oi 



