242 ON LIGHT. 



(25.) It is evident from what we said in the last para- 

 graph, that according to the greater or less disproportion 

 between the lines M R, N s, on the diagram there given, 

 or the sines of the two angles of incidence and refraction, 

 the greater or less will be the amount of bending (or 

 angle of deviation, as it is called) of the ray at its point of 

 transmission, for one and the same degree of obliquity 

 as also that for one and the same medium, the deviation 

 increases with the angle of incidence (though not propor- 

 tionally to *t) being nil when the ray enters perpendi- 

 cularly, and a maximum when just grazing the surface. 

 If in any case M R be greater than N s, or the " ratio of the 

 nines" be one of " greater inequality," the bending will be 

 towards the perpendicular ; if less, or if that ratio be one 

 " of less inequality," from it ; as indicated by the course 

 of the dotted ray in the figure. If the former be the case 

 in any instance, as in that where a ray passes out of air 

 into water, the latter will happen in the reverse case, as 

 where it passes out of water into air: that is to say, in 

 optical language, " out of a denser medium into a rarer." 

 This follows, from the general fact that the illuminating 

 and illuminated points are convertible, or that a ray can 

 always return by the path of its arrival, so that the re- 

 fraction of a ray out of any medium into air is per- 

 formed according to the same rule of the sines, only 

 reversing the terms of the proportion ; or in other words, 

 regarding what was the angle of incidence in the one 

 case as that of refraction in the other and vice versa. 

 Numerically expressed, this reversal of the terms of a 

 proportion, or ratio, is equivalent to inverting the numer- 



