Rob wrote:

>  "Arwachyll" is quite obviously "ar" + "bhachaill", which strickly
> interpreted would mean "battle of bachuil".  But I'm thinking that it
> more precisely translates as "battle-luck of bachuil".  

Perhaps this is simply 'battle-crosier' (cf. árchú, 'battle-hound'),
with the fairly common Middle Irish confusion of the dative (bachaill)
for the nominative? 

In Old and Middle Irish, genitive 'of a bachall' would be 'bachaille';
since bachall is a feminine á-stem. Had it changed declension in
Scotland by this time?

For the thaumaturgical use of crosiers in battle, cf the way in which St
Brigit single-handedly routed the Uí Néill armed only with her staff.
(Vitae Primae Sanctae Brigitae §88.6; Sean Connolly, Journal of the
Royal Society of Antiquaries of Ireland, vol 119 (1989) p 41.)