Okay,
The problem as I see it is that the Gospels are not explicit enough for us to definitively exactly what kind of Stauros Jesus was affixed to. I have the pdf of the Latin book the Society appeals to and one thing the book makes abundantly clear is that the Romans used a bewildering variety of cruxes for execution. The variety of cruxes each had their own particular form of suffering and humiliation and which one was used was generally up to the whim of the Roman administrator or executioner and just how they wanted to see the victim humiliated and tortured during their passing.
So, the society, largely for christophobic reasons (referring to Christendom rather than Jesus Christ himself) sticks to the dictionary definition from classic Attic Greek over other choices. Use of the word by contemporary Greek writers doesn't even appear to enter into the calculation as far as Leo seems to have documented so well. That is where we stand on that one.
Personally, I think one clue in the New Testament may give us something of an answer. The fact that after having victimized Jesus with a Roman scourging, the Romans still expected Jesus to be capable of carrying his stauros to Golgotha. That is quite a ways to carry a piece of wood.
I don't know about the rest of you, but I've worked clearing forested land and have an idea of just how heavy trees really are. Even a fairly narrow tree of the rough dimensions of steaks or crosses are pretty heavy things even after all the branches are cleared off. Consider that Jesus was weakened by having received no food or water from the time of his arrest to his execution, and further factor in the abused of a Roman "examination," torture by another name. Further factor in the scourging which traditionally preceded a crucifixtion, something we know was done to Jesus, and there is no way any human being would've been able to carry a cross or a stake as illustrated.
So the stauros Jesus was expected to carry had to be a patibulum. Anything else would've been to heavy for a person so abused to carry anywhere. However, the patibulum would still be heavy enough that the condemned would be so further weakened from the burden that they would not have been able to offer any significant resistance to when it came time to affix them to the instrument of execution. That is how I, in their position, would have done things. That Jesus was so weakened that he could not carry it any real distance is a testament to how extreme his examination and scourging really were.
So the most logical explanation to me is that he was crucified on a cross, rather than affixed to a stake. I don't see how one can logically arrive at any other conclusion.
Their is further potential evidence to ponder. The society makes much ado about the Jews insisting that the "stake" upon which a criminal was hung and displayed be buried with the victim in conformance with Jewish law. The Romans, ever the practical people, would likely have done something they are know to have done elsewhere. Place a permanent pole, or stake, in the ground at the usual place of execution, to which the would affix the patibulum and the victim. Otherwise, the cost of wood for crosses or full stakes would've likely been prohibitive. And the patibulum would've been just big enough to accomplish its purpose and small enough to be cost effective. That further leads one to the cross as the most likely stauros.
Respectfully
Forscher