Relative to the question of calculating the Part of Fortune only by the day formula or varying according to day or night formula, here is the actual documented history of the issue:
+the first recorded mention of a Part of Fortune (and a Part of Spirit) is found in Manilius' "Astronomica", AD 14; the instructions given there are to calculate by either the day or the night formula, according to the birth being in daylight, or at night.
+around 58 AD Dorotheus of Sidon ("Carmen Astrologicum") mentioned the Part of Fortune (note: the Greco/Roman astrologers used the term "Lot" rather than "Part") and, like Manilius, directed calculating either by the day or the night formula
+in the mid-2nd century AD Claudius Ptolemy mentioned the Part of Fortune; Ptolemy stated only one way to calculate it, by the day formula (whether born in daytime or at night) Ptolemy mentioned no other Lots (Parts) unlike other Greco/Roman astrologers, who mentioned numerous types of Lots in addition to the Part of Fortune
+until Islamic times, all Greco/Roman astrologers after Ptolemy continued to mention the Part of Fortune and all of them recommended using day formula for day births and night formula for night births
+in the 11th century Al-Biruni mentioned the Part of Fortune (and many other lots) and directed that the formula vary according to day or night
+in the 12th century Ibn Ezra mentioned the Part of Fortune (and many other lots); he specifically referenced Ptolemy, and claimed that "Ptolemy was correct" and that the Part of Fortune should be calculated only by the day formula.
+subsequently, close followers of Ptolemy use only the day formula for the Part of Fortune; the majority of subsequent astrologers followed (and continue to follow) the original (Manilius) instructions and calculated the Part of Fortune by day formula if a daytime birth, and by night formula if a nocturnal birth
+in early 2010 I conducted a poll on skyscript (this thread is still there in the traditional astrology section) relative to the question, "do use you day formula only or do you vary in calculating the Part of Fortune"; about 2/3rds of the respondents voted that they vary the fomula according to diurnal or nocturnal birth time...