122 ON A PROPERTY OF THE CAUSTIC BY REFRACTION OF THE CIRCLE. [124 
Theorem. The caustic by refraction of a circle when the radiant point is on the 
circumference, is the caustic by reflexion for the same radiant point, and a concentric 
circle the radius of which is the radius of the first circle divided by the index of 
refraction. 
C 2 
Again, if £ = - c/jl, the fifth system gives f' = |>, d = c, //,' = - 1, or the new system 
is in this case also a reflecting system. This is the other of M. St Laurent’s 
theorems, viz.:— 
Theorem. The caustic by refraction of a circle when the distance of the radiant 
point from the centre is equal to the radius of the circle multiplied by the index of 
refraction, is the caustic by reflexion of the same circle for a radiant point which is 
the image of the first radiant point. 
Of course it is to be understood that the image of a point means a point whose 
distance from the centre = square of radius 4- distance. 
2 Stone Buildings, Nov. 2, 1853.