The goal of the polarimetry of electromagnetic solids is the thorough determinations of not only the linear and circular birefringences (LB an CB) but also the linear and circular dichroisms (LD and CD). Needless to say, measurements of circular phenomena are exceedingly more difficult than those of linear ones. For instance, the long period of 170 years elapsed from the discovery of CB by Arago in 1811 until the development of high accuracy universal polarimeter (HAUP) by Kobayashi in 1983, when the first perfect measurements of CB of solids became possible. Subsequent to the appearance of the HAUP method, attempts of extending HAUP theory to be applicable to CD measurements were followed by Moxon and Renshaw, and Dijkstra, Kremers, and Meekes by using Jones matrix calculus. However, their measurements to NiSO4 multiplied by 6H2O were not fully satisfactory. We completed afresh the theory of the extended HAUP and measured successfully LD of a high temperature superconductor Bi2Sr2CaCu2O8. An important fact was clarified; the extended HAUP theory indicates that CD can be obtained exclusively through accurate measurements of (theta) 0, a characteristic angle introduced in the original HAUP method. It means that there would be no ways for measuring CD of solids except for the HAUP method. Preliminary results of applying our theory to silver thiogallate are shown finally.