All these details connected with dates, the list of which, down to the times of Camillus, might be vastly swelled, are so characterised by marks of inconsistency and historical impossibility, that it may safely be concluded that here we are entitled to the exercise of criticism. Let us now call to mind the twofold sources of the earliest Roman history,--the chronological ones, the Fasti, the _Annales Pontificum_; and the unchronological ones, the lays, _Laudationes_, the _Libri Pontificum_ and _Augurales_. With regard to the chronological ones, we see that in the oldest accounts of Fabius, from the building of Rome to its destruction by the Gauls, 360 years are reckoned; precisely the number of the γένη in Attica, which number the Greeks already (especially Aristotle, from whom the grammarians Pollux, Harpocration, and others borrowed) declared to have been in imitation of the solar year. If we look more closely into it, 360 is the middle number between those of the days of the solar and lunar year, and the nearest to either of these capable of being conveniently divided. The time assigned for the kings, according to the older reckoning, was 240 years; that for the republic, 120. This number has the same mathematical character as those of the Indian ages of the world, the Babylonian, and other eastern numbers. The 120 years for the republic are received also by those who deem the whole period to have been 365 years. Whether these 120 years are correct, remains indeed to be decided according to one’s views with regard to the epoch of the dedication of the Capitol. That the annals of the pontiffs were destroyed when the city was burned by the Gauls, is strongly confirmed by Claudius (without doubt Claudius Quadrigarius) in Plutarch, and indirectly by Livy, who cannot state it in a direct manner, or else he would have declared his first books to be worthless. An additional proof of it is the fact, that the eclipse of the sun in the year 350 was the first one really observed which occurred in the annals; whereas all the earlier ones were calculated afterwards, and of course incorrectly, with the aid of the scientific means which then existed. For the first 240 years we have seven kings, who reigned for an immense time, most of them about forty years. Newton has already pointed out how improbable it was, that a succession of princes should have all ruled for so long a period, and he has assigned seventeen years as an average for each. The most exact parallel, however, is to be found among the doges of Venice, who also were elective princes like the Roman kings. There have been forty doges within the space of five centuries (800 to 1300), so that there were eight of these to a century. When we now look more closely at the numbers of the Roman kings, we find in them a play upon numbers, as among the eastern nations. To understand this, we must premise the following remarks.