In the principles which the Karaites by and by were forced to lay down, in order, in a measure, to put a stop to the individualistic tendencies of their adherents, who were always forming new sects, they recognized the authority of tradition. They accepted the laws for slaughtering and the manner of fixing the beginning of each month, under their rule that a great many customs, not prescribed in either the Law, the Prophets or the Hagiographa, yet universally observed among the members of the Jewish race, were obligatory as religious practices. This rule of agreement or analogy was later called by them tradition (Haatakah) or hereditary teaching (Sebel ha Yerusha). In practice, however, they were arbitrary, inasmuch as they retained one custom as traditional, while they rejected others possessed of equal claims to be considered traditional. The rule of analogy led Karaism into new difficulties, especially as regards the marriage of certain blood-relations. They fell from one difficulty into another. They held that the affinity between a man and his wife was, according to the Bible, continuous. Consequently step-children should not be allowed to intermarry. But they went still further. The affinity between a man and his wife continues, they said, even if the marriage is dissolved. If in such a case the husband or the wife marries again, the affinity extends to the new families, although they are unknown to each other. Hence the members of the family of the first husband cannot intermarry with the members of the second husband's family. This affinity continues to the third and fourth generations. Thus the circle of affinity was considerably enlarged. The authors of this system of artificial relationship called it "handing over" (Rikkub, Tarkib). Why they should have stopped at the fourth generation it is difficult to see, but it appears that they feared the ultimate consequences. Such was the confusion in which Karaism had enveloped itself in its endeavor to break with the past. CHAPTER VI. FAVORABLE CONDITION OF THE JEWS IN THE FRANKISH DOMINIONS, AND THE DECAY OF THE EXILARCHATE IN THE EAST. The Jews under Louis le Débonnaire--The Empress Judith and her Veneration for Judaism--Agobard, Bishop of Lyons-- Conversion of Bishop Bodo--Amolo's effort against the Jews-- Charles the Bald--Troubles in Béziers and Toulouse--Decree against the Jews in Italy--Boso of Burgundy--Basilius-- Leo the Philosopher--Decline of the Exilarchate--The Geonim acquire Additional Influence--The Prayer Book of Amram-- Mar-Zemach--Literary and Scientific Activity of the Jews-- Decay of Karaism--Dissensions at Pumbeditha. 814-920 C. E.