This is why the Orthodox Churches which still use the old Julian Calendar continue to celebrate the Lord's Nativity on that date. They are in fact celebrating the 25th of December. They just ignored the Roman Pope's idea of deleting days from the calendar and prefer to use the calendar the Apostles and all the Empire used in Christ's time.
The Armenian Apostolic Orthodox Church alone continues the ancient practice of celebrating all of the events of the Lord's life prior to His baptism on the day of His Theophany (ie Epiphany). They "celebrate the Nativity of the Lord as part of the Epiphany on 6 January" (Liturgical and Ritual Issues and Proposals Concerning the Restoration of Communion, 2000, p. 28; by Deacon Dr. Emile [now Fr. Shenouda] Maher Ishak). On the Julian Calendar, the 6th of January falls on what the Gregorian Calendar reckons as the 19th of January.
In ancient times many of the Eastern Christian Churches followed the current practice of the Armenians. But from the time Christianity was legalised, the ability for Churches to communicate easily increased. The archives of Rome were opened and the census records confirmed the Lord Jesus Christ was born on the 25th of December. Since then the celebration of Christ's birth upon the 25th of December has been adopted by almost all Christians throughout the world. Even the Armenians accepted the separation of the two feasts for a short period but reverted to their current observance in the sixth century which they follow until now (Encyclopedia of Religion and Ethics, 1908-26, Vol. III, p. 605; by James Hastings).
This is roughly true. But Pachon is the ninth month of the ancient Egyptian calendar as shown in the table. Today, the Arabic-speaking Coptic Christians call it Bashans. Likewise, December was the ninth month of the Julian Calendar. New year was on March 25 so it was named "Dec"-ember because it was the tenth from the start of the year. But April was counted as the first month not the last week of March. Hence, December was commonly called the ninth month. This explains the confussion. Notably, St. Clement is aware of the confussion and so mentions various less popular supposed dates in his works, one of which includes the 25th of the following month.
The Extant Writings of Julius Africanus do however make reference to the date of Christ's crucifixion and the prophesies of Daniel.
III. - The Extant Fragments of the Five Books of the Chronography of Julius Africanus section XVI. On the Seventy Weeks of Daniel.
Part 1 "...the passage speaks of the adent of Christ..." "And the beginning of the numbers, that is, of the sevty weeks which make up 490 years, the angel instructs us to take from the going forth of the commandment to answer and to build Jerusalem.. And this happened in the twentieth year of the reign of Artaxerxes king of Persia." (see also Daniel 9:24-7, Ezra 7:9, Nehemiah 2:1)
Part 2 "And at that time King Artaxerxes gave order that the city should be built.... And reckoning from that point, we make up seventy weeks to the time of Christ."
Part 3 "It is by calculating from Artaxerxes, there, up to the time of Christ that the sevnty weeks are made up, according to the numeration of the Jews."
The latter reference to "the 16th year of the reign of Tiberius Cæsar... which make 490 according to the Hebrew numeration" equates to the year 30 A.D. This being the case, it does not refer to the birth of Christ. So unless there is some other passage in his writings (whether extant or extinct) which may identify the date of the Lord's birth, he has shown nothing more than what Tertullian showed. That is, important dates could be calculated based upon available information in the early centuries after our Lord's advent.
Note: This page is to be updated as time permits.