Late Roman Legion size based on the Perge Inscription

[FlaviusB]

800 Munifices plus the 1245 officers and men listed on the inscription adds up to 2045; tripling this number gets us to 6135... I split the 275 Veredari into 5 Turmae of 55 with 10 Veredari and 45 Veredari Alii each, while each 'maniple' of two centuries has an Optio, Vexillarius, Imaginifer and Signifer. 

73 Clerici et Deputati, the latter of which can be distributed in a way that makes sense with this structure...

Well done for engaging with this question, and for making the numbers work (as far as I can see, anyhow!) - it does become a little maddening after a while... I'm impressed that you figured in the clerici et deputati too; I confess I'd discounted them, as they're supernumeraries with no annonae, and besides I'm not sure if the number 73 is accurate (the inscription itself is so fragmentary at that point I cannot make out what Prof Onur was drawing on!)

Getting the 'veredarii' cavalry (if that's what they were) into a balanced structure is one of the main difficulties with the Perge list. Dividing them into five turmae might work. The problem would be that we do not have five decurion-type officers to command them, or five standard bearers either. And 55 is a very large turma.

All the officer, nco and standard-bearer ranks on the list, meanwhile, are in 10s. That suggests to me that the complete organisation was decimal. However, as you point out, many of the internal numbers break down by 8s and 16s.

My own theory, outlined on the years-old thread you linked, would be a paired 'numerus' of ten infantry and ten cavalry subunits, each commanded by an ordinarius. It's not a perfect system by any means. But I still like it for several reasons. Firstly as both the infantry and cavalry complement appear close to the estimates for late Roman units of their type (c.1200 and c.300 respectively). Secondly because we can see the core of the old principiate 80-man century still preserved in the enlarged 110-man 'mini cohort'. Thirdly because Vegetius says that a century (in his day, perhaps?) was 110 men - an otherwise-inexplicable comment!

So, while I still don't think after all this time that this is the only possible solution to the Perge enigma, it does at least seem a close-ish fit to the limited evidence we have from elsewhere:

My thinking, which you may have read already in the older thread, is that the 45 Veredarii Alii in each Turmae would be divided into 5 files of 9, while the 10 Veredarii could be divided into 5 'file leaders' giving each file 10 men in total and the other 5 are a headquarters. I should also note that 6 of these 55-man Turmae plus a larger headquarters staff would get us close to the 360 number mentioned by Julian in his letter to the Athenians, and the 350 figure implied by Ammianus for Late Roman Cavalry regiments.