Diese Veränderungen für je zwei differirende Merkmale zu beobachten und das Gesetz zu ermitteln, nach welchem dieselben in den aufeinander folgenden Generationen eintreten, war die Aufgabe des Versuches.
To observe these changes for two differing traits respectively, and to investigate the law according to which they occur in the successive generations, was the task of the experiment.
two differing traits respectively = je zwei differirende Merkmale As in the previous sentence, Mendel is referring to character pairs here. Bateson has “each pair of differentiating traits”. On the term differirend, see p. 3, s. 8.
law = Gesetz See p. 3, s. 6. Mendel formulates his aim very clearly in this sentence. His use of the definite article for “successive generations” indicates that he was interested, above all, in the law that governs transmission in the descendants of hybrids (see p. 3, s. 8). Gärtner had formulated the conjecture that one should be able to find “laws of formation” (Gesetze der Formbildung) for descendants of hybrids, a statement that Mendel marked in his copy of Gärtner’s book (see Carl Friedrich Gärtner, Versuche und Beobachtungen über die Bastarderzeugung im Pflanzenreich (Stuttgart: Hering, 1849), Mendel Museum, Collection of the Augustinian Abbey, p. 272.
generations = Generationen See p. 3, s. 8.