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incident on a polished surface, and the direction of the ray is from 

 the more dense, towards the rarer medium (as from glass towards 

 air for instance), when the obliquity of the incident ray reaches a 

 certain point, the whole of the light is reflected, and none of it is 

 transmitted. Now this is precisely the condition it is desirable to 

 arrive at in the two internal reflections in the prisms under consider- 

 ation. It is worthy of observation, that, provided the angle of the 

 incident ray be sufficient to cause total reflection, there is no 

 objection to its being somewhat more, though a less degree of 

 obliquity would defeat the object. 



The angle of obliquity, in order to produce the effect of total 

 reflection, differs in the various kinds of glass (principally according 

 to the density), and it also differs for the various coloured rays of 

 the spectrum. If, however, an inclination of forty-five degrees be 

 given, this is amply sufficient to cause total reflection for rays of 

 every colour in any of the ordinary kinds of glass. 



Keferring to figs. 8, 4, 5 and 6, the ray z A, after its first 

 reflection at w> must follow the course of one of the lines, w v, 

 previously to its second reflection at v ; that is to say, the course 

 must be such as to make the angles z w A and w v A, either both 

 acute angles, as in fig. 3, or the former a right angle and the latter 

 acute, as in fig. 4, or the former obtuse and the latter a right angle, 

 as in fig. 5, or, lastly, both obtuse angles, as in fig. 6. Now in the 

 two former cases, figs. 3 and 4, it is manifest that, at one at least of 

 the reflections, the inclination of the incident ray is insufficient to 

 cause total reflection : it therefore only remains to decide between 

 figs. 5 and 6, in both of which the inclination at both angles is 

 sufficiently great. 



There are two reasons which induce me to select fig. 5 in 

 preference to fig. 6, while I know of none in favor of the latter. 

 Firstly, fig. 5 does not require the prism to be so great in length as 

 fig. 6 would ; and secondly, by adopting fig. 5 a general set of 

 formula? for constructing prisms, for any obliquity, can be readily 

 framed. Another objection that has been made to my adopting 

 forty-five degrees for the angle q, figs. 1 and 2, I think it right to 

 answer in this place, viz., that if moisture were condensed on the 

 sides of the prism, the obliquity would not be sufficient to prevent 

 the ray being refracted out of it. My answer is, the remedy is 

 simple ; by wiping off the moisture (the prism can readily be mounted 

 so as to allow of this being done), and, what is perhaps a more 

 decisive reply, the same objection will apply to any angle that it is 

 practicable to adopt, for unless the obliquity of the internal incident 



