

THE SENSORIAL FUXCTIO^fS. 



liquity of the ray to the surface which refracts it; and is 

 mathematically expressed, by the law that the sines of the 

 two angles formed with the perpendicular by the incident 

 and the refracted rays retain, amidst all the variations of 

 those angles, the same constant proportion to one another. 

 We may hence derive a simple rule for placing the plane of 

 the refracting surface so as to produce the particular refrac- 

 tion we wish to obtain. When a ray is to be deflected from 

 its original course to a particular side, we have only to turn 

 the surface of the medium in such a manner as that the per- 

 pendicular line to that surface, contained within the denser 

 medium, shall lie still farther on the same side. Thus, in 

 Fig. 408, if we wish to turn the ray r s, from s o to s t, we 

 must place the dense medium so that the perpendicular s p, 

 which is within it, shall be still farther from s o,than s xis; 

 that is, shall lie on the other side of s t. The same rule ap- 

 plies to the contrary refraction of the ray s t from t v to t 

 u, when it passes out of a dense, into a rare medium; for the 

 perpendicular t i must still be placed on the same side of 

 T V as T u is situated. 



Let us now aj)ply these principles to the case before us; 

 that is, to the determination of the form to be given to a 

 dense medium, in order to collect a pencil of rays, proceed- 

 ing from a distant object, accurately to a focus. We shall 



409 



•B 



suppose the object in question to be very remote, so that 

 the rays composing the pencil may be considered as being 

 parallel to each other; for at great distances their actual de- 



