The investigation of this question upon the elastic solid theory will depend upon how we suppose the solid to vary from one optical medium to another.
So long as the particles are supposed to be very small and to differ little from their environment in optical properties, there is little difference between the electric and the elastic solid theories, and the results expressing the character of the scattered light are equivalent to (5).
We learn that the light dispersed in the direction of primary vibration is not only of higher order in the difference of optical quality, but is also of order k 2 c 2 in comparison with that dispersed in other directions, where c is the radius of the sphere, and k=21r/X as before.
In the optical examination we may, if we prefer it, polarize the primary light; but it is usually more convenient to analyse the scattered light.
Of lost works by Archimedes we can identify the following: (I) investigations on polyhedra mentioned by Pappus; (2) Archai, Principles, a book addressed to Zeuxippus and dealing with the naming of numbers on the system explained in the Sand Reckoner; (3) Peri zygon, On balances or levers; (4) Kentrobarika, On centres of gravity; (5) Katoptrika, an optical work from which Theon of Alexandria quotes a remark about refraction; (6) Ephodion, a Method, mentioned by Suidas; (7) Peri sphairopeoia, On Sphere-making, in which Archimedes explained the construction of the sphere which he made to imitate the motions of the sun, the moon and the five planets in the heavens.