If we afterwards intercalate new steps according to the law of formation of incommensurable numbers, we shall obtain what we will call a continuum of the second order.
Just so, as soon as we have been led to intercalate means between two consecutive terms of a series, we feel that this operation can be continued beyond all limit, and that there is, so to speak, no intrinsic reason for stopping.
But this is not yet enough; between these terms, which, however, are already infinite in number, it is still necessary to intercalate others called irrational or incommensurable.
Let us start from the scale of whole numbers; between two consecutive steps, intercalate one or more intermediary steps, then between these new steps still others, and so on indefinitely.
So far it would suffice, in accounting for the facts, to intercalate between A and B a few terms, which would remain discrete.
As often as he meets with new groups, he must ascertain by superposition their age relatively to those first examined, and thus learn how to intercalate them in a tabular arrangement of the whole.
In this case, the palaeontologist is called upon suddenly to intercalate about 800 species of Mollusca and Radiata, between the fauna of the Lower Lias and that of the Middle Trias.
In order to keep the sequence of months in the arrangement given above in accordance with the moon, it becomes necessary to intercalate one more day every two repetitions of the 3986 period.
By this reformation, says Dion Cassius, all error was avoided except a very small one, and he adds, that to correct the accumulations of this error, it would only be necessary to intercalate one day in 1461 years.
The rule was to intercalate a day in every fourth year (quarto quoque anno).
