That there exists a point such that the tangents from this point to the four spheres are equal, and that with this point as centre, and the length of the tangent as radius, a sphere may be described which cuts, the four spheres at right angles; this "**orthotomic**" sphere corresponds to the orthogonal circle of a system of circles.

Secondary caustics are **orthotomic** curves having the reflected or refracted rays as normals, and consequently the proper caustic curve, being the envelope of the normals, is their evolute.