With regard to the intercalation, the equalising of the total number of moon-months and the solar year, the problem first arose when there had been developed a fixed series of months which it was desired to repeat without interruption. Then arose the necessity of introducing an occasional month into the series of twelve months, or omitting one from the series of thirteen, so that the months named from natural phases might remain in their proper places. This difficulty was first of all blended with that arising from the fluctuation of the natural phases due to the varying climatic conditions of different years. The expedient was crudely empirical, the occasional leaping over or addition of a month. Gradually it became the custom to introduce the intercalary month at a definite point; it may also be associated with a so-called ‘vacant period’. Where a month was named from a phase of a certain star, the correction was given automatically by this phase, since this month was fixed. The intercalary month obtained its place before this month, which became the beginning of the year, since the reckoning started with it. By this means was given a lunisolar year which was however empirically regulated by occasional intercalation. APPENDIX: THE EGYPTIAN YEAR. Upon the quite peculiar Egyptian time-reckoning I have only a few remarks to make by way of addition to the clear and convincing account of its origin given by Eduard Meyer; as to the disarrangement of the names of months familiar to us, which are borrowed from festivals, I must admit I am not quite clear, but this matters little for our present purpose since these names are more than two thousand years younger than the introduction of the year. The Egyptian year consists of three seasons--time of inundation, seed-time, and harvest--each of four months containing thirty days each, together with five additional days, the epagomena, standing outside the year and theoretically not included in it. The month is therefore the round month and the year the round year, which by multiplying the round number of the months in the year by the round number of days in the month gives a total of 360 (12 × 30) days. The use of round numbers in the arithmetical application of the calendar is familiar in all quarters of the world and has been known at all times; it is continued in the practice of our modern banks in calculating interest _à l’usance_. The surprising thing is that in Egypt no notice should have been taken of the moon, and that the month should have been carried through as a mere numerical unity. For at the stage of knowledge presupposed by the regulation of the calendar the Egyptians must have known that the number of days in the moon-month varies between 29 and 30. I am therefore inclined to think that this form of year was first introduced as a means of counting in administration and the making of returns, and then by degrees established itself as the civil calendar because the