It is further to be noted that the same kind of change which now happened to the Christian Empire, had happened earlier in the century to the Mahometan Empire. The establishment of a rival dynasty at Cordova, even though the assumption of the actual title of Caliph did not follow at once, was exactly analogous to the establishment of a rival Empire in the Old Rome. The Mediterranean world has now four great powers, the two rival Christian Empires, and the two rival Mahometan Caliphates. Among these, it naturally follows that each is hostile to its neighbour of the opposite religion, and friendly to its neighbour’s rival. The Western Emperor is the enemy of the Western Caliph, the friend of the Eastern. ♦Rivalry of the Empires and Caliphates.♦ The Eastern Emperor is the enemy of the Eastern Caliph, the friend of the Western. Thus the four great powers stood at the beginning of the ninth century. And it was out of the dismemberments of the two great Christian and the great Mahometan powers that the later states, Christian and Mahometan, of the Mediterranean world took their rise. ♦Extent of the Carolingian Empire.♦ It is a point of geographical as well as of historical importance that Charles the Great, after he was crowned Emperor, caused all those who had been hitherto bound by allegiance to him as King of the Franks to swear allegiance to him afresh as Roman Emperor. This marks that all his dominions, Frankish, Lombard, and strictly Roman, are to be looked on as forming part of the Western Empire. Thus the Western Empire now took in all those German lands which the old Roman Emperors never could conquer. Germany became part of the Roman Empire, not by Rome conquering Germany, but by Rome choosing the German king as her Emperor. ♦Contrast of its boundaries with those of the elder Empire.♦ The boundaries of the Empire thus became different from what they had ever been before. Of the old provinces of the Western Empire, Britain, Africa, and all Spain save one corner, remained foreign to the new Roman Empire of the Franks. But, on the other hand, the Empire now took in all the lands in Germany and beyond Germany over which the Frankish power now reached, but which had never formed part of the elder Empire. ♦Conquest of Saxony. 772-804.♦ The long wars of Charles with the Saxons led to their final conquest, to the incorporation of _Saxony_ with the Frankish kingdom, and, after the Imperial coronation of the Frankish king, to its incorporation with the Western Empire.