Now, then, in the highest spirits, let us open our studies. And first let us map out a chart of the _personnel_ for pretty nearly a century. Twelve Caesars--the twelve first--should clearly of themselves make more than a century. For I am sure all of you, except our two new friends, know so much of arithmetic as that multiplication and division are a great menace upon addition and subtraction. It is, therefore, a thing most desirable to set up compound modes--short devices for abridging these. Now 10 is the earliest number written with two digits: and the higher the multiplier, so much harder, apparently, the process. Yet here at least a great simplification offers. To multiply by 10, all you have to do is to put a cipher after the multiplicand. Twenty-seven soldiers are to have 10 guineas each, how much is required to pay all twenty-seven? Why, 27 into 10 is 27 with a cipher at the end--27:0, _i.e._, 270. _Ergo_, twelve Caesars, supposing each to reign ten years, would make, no, _should_ make, with anything like great lives--12:0, _i.e._, 120 years. And when you consider that one of the twelve, viz., Augustus, singly, for _his_ share, contributed fifty and odd years, if the other eleven had given ten each that would be 11:0; this would make a total of about 170. VIII.--_Beginning of Modern Era._--From the period of Justinian commences a new era--an era of unusual transition. This is the broad principle of change. Old things are decaying, new things are forming and gathering. The lines of decay and of resurrection are moving visibly and palpably to every eye in counteracting agency for one result--life and a new truth for humanity. All the great armies of generous barbarians, showing, by contrast with Rome and Greece, the opulence of teeming nature as against the powers of form in utter superannuation, were now, therefore, no longer moving, roaming, seeking--they had taken up their ground; they were in a general process of castrametation, marking out their alignments and deploying into open order upon ground now permanently taken up for their settlement. The early trumpets, the morning _reveille_ of the great Christian nations--England, France, Spain, Lombardy--were sounding to quarters. Franks had knit into one the rudiments of a great kingdom upon the soil of France; the Saxons and Angles, with some Vandals, had, through a whole century, been defiling by vast trains into the great island which they were called by Providence to occupy and to ennoble; the Vandals had seated themselves, though in this case only with no definite hopes, along the extreme region of the Barbary States. Vandals might and did survive for a considerable period in ineffective fragments, but not as a power. The Visigoths had quartered themselves on Spain, there soon to begin a conflict for the Cross, and to maintain it for eight hundred years, and finally to prevail. And lastly, the Lombards had thrown a network of