the one calendar correspond to those of the other, and this is the case, since the week came to Iceland from the south. Bilfinger is not correct in calling (I, 71) the shifting Easter period a fragment of a week-year: in so doing he shuts his eyes to what he himself terms the quinary factor, i. e. that Easter Sunday falls varyingly on one of the five Sundays between March 22 and April 25 (the other days of the Paschal term being fixed accordingly). This fact, as has long ago been observed, makes the Easter period a fragment of a lunisolar year. A further development would lead to a lunisolar year that also took into account the reckoning in weeks. Bilfinger’s view of the matter is that the Icelanders for the sake of convenience eliminated the quinary factor from the Easter reckoning by taking the mean Easter Thursday as a fixed point of departure instead of letting the calendar follow the actual variation of this day: this roundabout method is unnecessary since the same result is arrived at by basing a system of time-reckoning on the year and the week. The aim of the Icelandic calendar, according to Bilfinger, was to fix the beginning of summer, a legally very important term. If this was the object in view it was, as Brate remarks (p. 21), not attained, for this day, Thursday of the week April 9-15, may fall in the Passion week so that it becomes useless for all business purposes. This proves on the contrary that the fixing of the beginning of summer is pre-Christian. The last objection to Are’s account of the introduction of the Icelandic calendar, which Finnur Jonsson and Brate have allowed to stand, must also fall. According to Are the cyclical interpolation of a week was introduced by Torsten Surt about 960 A. D., while previously the year had 52 weeks, i. e. 1¼ days too few. Bilfinger objects that such a year is unthinkable, since in the course of 40 years it must anticipate itself by 50 days, and therefore in 292 years must have run through the whole circle of the seasons: the mid-winter festival must therefore for one generation have fallen in summer. Theoretically the objection is valid, but in practice not so (cp. the Egyptian shifting year), and the old calendars are administered practically. In the effort to arrive at an embolimic cycle mistakes are at first made, and the agreement with the solar year is once more brought about by means of intercalations irregularly introduced for practical reasons. How the ancient Roman calendar was treated we know: by the end of the Republic it had become thoroughly disorganised as a result of intercalations made for political purposes. Moreover the Roman year with its average length of 366¼ days was from the beginning not a whit better than the year of 364 days ascribed by Are to the Icelanders before Torsten Surt. We learn from inscriptions that in Athens still more irregular intercalations were made during the last decades of the 5th century. Such intercalations are the ruin of any system, but