Packing of incongruent circles on the sphere

In this paper we provide an upper bound to the density of a packing of circles on the sphere, with radii selected from a given finite set. This bound is precise, e.g. for the system of incircles of Archimedean tilings (4,4, n) with n greater than or equal to 6. A generalisation to the weighted density of packing is applied to problems of solidity of a packing of circles. The simple concept of solidity, was introduced by L, Fejes Toth [6]. In particular, it is proved that the incircles of the faces of the Archimedean tilings (4,6,6), (4, 6, 8) and (4, 6, 10) form solid packings.