Lactantius states that, in the night before the battle, Constantine was commanded in a dream to "delineate the heavenly sign on the shields of
his soldiers" (
Commonitus est in quiete Constantinus, ut caeleste signum Dei notaret in scutis atque ita proelium committeret).
He obeyed and marked the shields with a sign "denoting
Christ".
Lactantius describes that sign as a "
staurogram", or a Latin
cross with its upper end rounded in a P-like fashion, but there is no certain evidence that Constantine ever used that sign (
Staurogram 
) or the better known
Christogram (
which is described by Eusebius) on the shields.
Both Lactantius and Eusebius were
writing after the event, in the case of Eusebius, 25 years after and in
his case Eusebius' detailed description of the
Chi-Rho was in reference to the manufacture of the
standard or "
labarum" not the sign carried on the shields of the soldiers.
In the case of Lactantius, who wrote a year or so after the event, according to Schaff, the account from Lactantius has been questioned by Burckhardt to have actually been composed by Lactantius himself, especially since he attributed a similar vision to Licinius (Chapter 46).
What is not in dispute is that the soldiers inscribed some symbol on their shields.
In the vision of Constantine "
He said that about noon, when the day was already beginning to decline, he saw with his own eyes the trophy of a cross of light in the heavens, above the sun, and bearing the inscription, Conquer by this. At this sight he himself was struck with amazement, and his whole army also, which followed him on this expedition, and witnessed the miracle. (1.28)"
Now Constantine
had had a similar vision previously, described in the Panegyrici Latini, which is dated to A.D.310 or 311 and which took place before a battle with the Franks. "
For, O Constantine, you saw, I believe, your protector Apollo (Sol Invictus), in company with Victory, offering you laurel crowns ....."
As
Robert has stated, Constantine's army was largely pagan, and Constantine himself up to this point
had adopted
Apollo or
Sol Invictus as
his patron deity, so I think that the heavenly symbol inscribed on the
shield was ambiguous and could be perceived as being the symbol of either
Sol or of
Christ. The symbol that best fits the bill is simply a
cross, like that of St. Andrew. This symbol scratched or painted on the shields of the soldiers would be the heavenly symbol of
Sol to the pagans and, to the Christians, the first two letters of Christ's name (Ch in Latin, translated into X in Greek).
Furthermore I think that there is actually overlooked numismatic evidence that this was the symbol employed. Witness the coin below with the enigmatic
reverse often described as the most unlikely "plan of a camp". This simple
cross is a symbol which could easily have been scratched or painted on a
shield and it is furthermore surmounted by the figure of
Sol which indicates to me, on this coin at least, that the sign is in some way attributable to him.
Alex.
