I have found the full Latin of the inscription which Roll (“Toward the Origins of Christmas”) implies states that Emperor Aurelian set up a feast for Sol Invictus on December 25 in 274AD. The Latin inscription can be found here (it is a transcription, sadly no picture is provided) it is number 580 (Inscriptiones Latinae Selectae by Hermann Dessau.) As we will see the inscription says no such thing about December 25:
Below I have transcribed it:
Soli invicto sacr.
pro salute et inco
imp. Caes. L. Domi
ti Aureliani Pii Fel.
Aug. p.m., t. p. VI, cos.
III, p. p., proconsuli[s]
Here is my translation:
To the Holy Unconquered Sun
for welfare and secur-
-ity of the perpetual
Emperor Caesar Lucius Domi-
-tius Aurelian the Pius Auspicious
Augustus Pontifex Maximus, earned title of consul 6 (times)
3 (times) [don't know what "p. p." is] procunsul
In my haste I am not too sure about the last line and the latter half of the 2nd to last. For help with Latin abbreviations in inscriptions see here
This inscription doesn’t tell us anything about when the feast was celebrated or even that Aurelian set up a feast at all. I suspect that this may have all been made up.
After some searching I found a nice blog about Sol Invictus by Roger Pearse, which lead to this wonderfully large and detailed dissertation on the cult of Sol by Steven Hijmans, our part of interest is here.
“there is no evidence that Aurelian instituted a celebration of Sol on that day [December 25]. A feast day for Sol on December 25th is not mentioned until eighty years later, in the Calendar of 354 and, subsequently, in 362 by Julian in his Oration to King Helios” [p.588 & p.6 of pdf]
So indeed, no evidence that Aurelian set up a feast for Sol Invictus on December 25, what of the other two pieces of evidence? The Philocalian Calendar (part 6 of the Chronography of 354) says that “Natalis Invicti” or “Birth of the Unconquered) was celebrated on December 25, whether that refers to Sol or Jesus is unclear, what is clear is that other feasts of Sol are mentioned by name (for example on August 28) and that the Chronography of 354 does say that Jesus was born on Dec. 25 in part 12.
The second piece of evidence is from no less than Julian the Apostate who in the late 4th century (Oration to King Helios IV, 156C from Hijmans p.589 & p.7 of pdf) claimed that Numa himself instituted a festival of Sol on December 25, meaning that for almost 1,000 years no one mentioned these celebrations until the 4th century, which casts much doubt upon the accuracy of this claim (especially given that it comes from a hostile source). Hijmans himself dismisses it on p.589 & p.7 of the pdf.
So to conclude our recent blog posts on Christmas and Roman festivals:
A feast to Sol Invictus (the Unconquered Sun) did occur on December 25, but the earliest evidence for it dates from the mid to late 4th century. There is no evidence that Emperor Aurelian established a Festival of Sol Invictus (or anyone or anything else) on December 25.
Egyptians apparently presented an infant as a representation of the newborn Sun on the winter solstice, but this evidence also dates from the fourth and fifth centuries.
Hippolytus in 202-211 AD set the date for the birth of Jesus on December 25, because he thought Jesus was conceived 9 months earlier on the Passover, the day in which he also thought the world was created (5500 years earlier), the Vernal Equinox March 25.
Clement of Alexandria (193-215 AD) quoted various anonymous sources about the birth of Jesus and roughly agrees with Hippolytus, claiming that Jesus was born in late fall to early winter. Clement’s sources clearly seem to believe that Jesus was conceived on the Passover and was born roughly 9 months later; in fact the only difference between them and Hippolytus is that they differed on when the Passover actually occurred. However there is a significant possibility that one of Clement’s sources was Hippolytus himself because of the preponderance of possible dates he gives that fall on the 25th of a month (He gives 4 of them and then another date on the 24th) which corresponds with Hippolytus’ belief that Jesus was both conceived, born, and executed on the 25th of a month.