The foundation of variable-star astronomy as an exact branch of the science is due to Argelander. In the years 1837-1845, while residing at Bonn during the erection of the observatory, of which he had been made director, he erected a temporary observatory, and there he carefully determined the magnitudes of all stars visible in Central Europe. From this he was led to the discussion of stellar variation, to which subject he continued to give much attention. He was the first to describe a method of observing variable stars scientifically and accurately,—a method consisting in estimating in “steps” or “grades” the difference in brilliance between the variable, or suspected variable, and other stars which are selected for comparison, and which are of various degrees of brilliance, so that they may be available for comparison with the variable throughout its fluctuations. Argelander’s “steps” are tenths of a magnitude, and Gore describes the method of observation as follows: “If we call _a_ and _b_ the comparison stars, and _v_ the variable, _a_ being brighter than _b_, and if _v_ is judged to be midway in brightness between _a_ and _b_, we write _a_5_v_5_b_. If _v_ is slightly nearer to _b_, we write _a_6_v_4_b_. We may also write _a_3_v_7_b_, or _a_7_v_3_b_, the sum of the steps being always ten.” This method, described in 1844, led to many discoveries at Bonn in the following twenty years by Argelander and his assistants Schmidt and Schönfeld. At this time Eduard Heis (1806-1877), at Münster, who also ranks as one of the founders of meteoric astronomy, while engaged on the construction of his great atlas, attentively determined the change of magnitude of stars visible to the naked eye; and by means of the naked eye, the opera-glass, and a small telescope, he amassed a large number of observations. At the same time two English observers, Hind and Pogson, were making remarkable discoveries which greatly increased the number of known variables. Among Hind’s discoveries were S Cancri of the Algol type; while Schmidt discovered another of the same class, δ Libræ, and also the famous ζ Geminorum. While director of the Observatory of Mannheim, an institution equipped with very antiquated instruments, Schönfeld devoted himself to the study of variable stars, and increased the number of known variables considerably. In the southern hemisphere Gould, in South America, did for the observation of variable stars what Argelander did in the northern.