I'm in the midst of re-reading Alfred P. Smyth's translation - the reference is found in Chapter 76, here's the sentence:
...the attacks of the Pagans and the daily illnesses of his body, did not leave off from presiding over the government of the kingdom; engaging in every art of hunting; instructing all his goldsmiths and craftsmen, falconers, hawk-handlers and dog-handlers ...
Did "falconarios" and "accipitrarius" represent two different branches or "arts" of Falconry? How were they different?
Oggins’s book, one of few standard in this topic (medieval falconry), seems to interpret these two words as two distinct group of people, distinguished by the type of the bird of prey they took care of, as following: '......This show that Alfred was interested in and skilled a distinction was made between the men in charge of king's falcons (falconarii) and those who took care of his hawks (accipitrarii)' (Oggins 2004: 40).
As for the distinction between a hawk and a falcon, he also cites the following letters from the correspondences between Boniface and Anglo-Saxon rulers in the middle of the 8th century, discussed earlier in his book (Oggins 2004: 38):
These two letters suggests that falcons were regarded as more special sort of bird of prey among other (more general) hawks, much more skilled in hunting, at least in pre-conquest England (To tell the truth, I had initially assumed that these two words, falconarii and accipitrarii are employed almost just as synonyms, as they were in some sources in the 12th and 13th centuries and the former was much more common).
Oggins further notes that the hawker (accipitrari) in medieval sources should have been translated as a keeper of hawks, in contrast to the newer meaning as a peddler of hawks since the 16th century (Cf. The Middle English Dictionary, 7: 526-7; OED, 7:25; Oggins 2004: 151, note 31).
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