[332] Pfannenschmid, _Germanische Erntefeste_, Hanover, 1878, maintains that the quadripartite division was developed alongside of the tripartite, and bases his statement on a study of the principal festivals. [333] _Om en nordisk årstredelning_, p. 248. I cannot however agree with the author in the direction indicated by the sub-title of his essay: “Is a trace of an old Germanic tripartite division of the year to be observed in our popular festivals?” [334] Above, p. 73. [335] For exceptions see Bilfinger, I, 8 ff. [336] Bilfinger has brought forward his opinion with great penetration and wide learning, but his reasoning cannot stand before a searching criticism such as that amassed by Ginzel, III, 58 ff., and Brate, _Nordens äldre tideräkning_, Program of the Södermalm College, Stockholm, 1908, pp. 17 ff., and in particular developed and more profoundly based by Beckman, _Alfræði_, Intro. pp. 1 ff.; cp. an article by the same author in the Norwegian periodical _Maal og Minne_, 1915, p. 198. I might content myself with a simple reference to Beckman, since I agree with him on all important points, but as his article is written in Swedish and is therefore probably inaccessible to many, I add the following note which in the main was written long before it now appears, originally in connexion with my studies in the primitive history of the Christmas festival, worked out in the year 1914. In point of fact it seems as though the objection which Bilfinger in his study of the Yule-tide festival, II, 120, note, makes against the criticism of Finnur Jonsson has not been answered (before Beckman): the objection is that no notice is taken of the fundamental idea of Bilfinger’s work on the Old Icelandic year--the cardinal point around which his whole demonstration revolves--viz. the relation of the Old Icelandic calendar to the calculation of Easter. Granting that the still heathen Icelanders or Norwegians knew the week (the Germanic peoples took over the week while yet in their heathen period, see my _Studien zur Vorgeschichte des Weihnachtsfestes_, Archiv f. Religionswiss., 19, 1918, p. 118) and made use of it in counting time, and that they later learnt approximately to know the length of the year--which is very easily conceivable in view of their lively intercourse with other nations--we have the elements out of which their calendar was developed, viz. the week and the year. To these must be added the old-established divisions of the year, summer and winter, which, on account of their importance for civil life, were introduced as fixed periods of time into the calendar. As a result of the adjusting of the reckoning in weeks to the year of 365, in leapyear 366, days, there arose a week-year with periodic interpolations of an embolimic week. This of necessity agrees with Bilfinger’s so-called ‘mean Easter year’, since both are constructed out of the same elements, it being assumed only that the week-days of