The 9/30 post at http://www.fivedoves.com/letters/sep2006/mattk930-1.htm states"6) The Western Roman Empire was the kingdom that "was" as John wrote. 7) The Eastern Roman Empire--Byzantium--was the kingdom which was to come, and we know it continued "for a short space" (till 788 AD). The iron legs of the image thus represent Rome in its eastern and western aspects."
(However, I don't see how the Byzantine Empire was the kingdom which was to come when the Eastern part of the Roman Empire wasn't renamed the Byzantine Empire until 1557, and it was in 1453 that it was conquered by the Ottoman Turks. It looks the the Ottoman Turk's Empire was the kingdom to come.)In regard to the Name of the Byzantine Empire, the article atstates the following:The Empire's native Greek name was Rōmanía, or Basileía Rōmaíōn, a direct translation of the Latin name of the Roman Empire, Imperium Romanorum. The term Byzantine Empire was introduced in western Europe in 1557, inspired from the city of Byzantium by German historian Hieronymus Wolf about a century after the fall of Constantinople who had taken it from the writing of 15th century Byzantine historian Laonicus Chalcocondyles. He presented a system of Byzantine historiography in his work Corpus Historiae Byzantinae, in order to "distinguish ancient Roman from medieval Greek history without drawing attention to their ancient predecessors".Standardization of the term began gradually in the 18th century, when French authors such as Montesquieu began to popularize it. Hieronymus himself was influenced by the rift caused by the 9th century dispute between Romans (Byzantines as we render them today) and Franks. The Franks under Charlemagne's newly formed empire, and in concert with the Pope, attempted to legitimize their conquests by claiming inheritance of Roman rights in Italy. The Donation of Constantine, one of the most famous forged documents in history, played a crucial role in this. Henceforth, it was prevalent in the West to refer to the emperor in Constantinople not by the usual Imperator Romanorum (Emperor of the Romans) which was now reserved for the Frankish monarch - a slight to the Byzantines as it threatened their sovereignty, but as Imperator Graecorum (Emperor of the Greeks) and the land as Imperium Graecorum, Graecia, Terra Graecorum or even Imperium Constantinopolitanum.