Was wondering the same thing, interestingly on the same day/evening as your second responder, looks like...but since what I see here didn't fully answer my question anyway, here's a bit more that seems like it does.
Apparently technically what holmes uses is actually abductive reasoning, as distinct from either deductive or inductive: http://en.wikipedia.org/wiki/Sherlock_Holmes#Holmesian_deduction
(at least according to that wiki-emergent article, which sounds fairly connected and supported so far in my understanding anyway).
And the linked article on the abductive type breaks down the differences as well: http://en.wikipedia.org/wiki/Abductive_reasoning#Deduction.2C_induction.2C_and_abduction
My guess is they kind of overlap or at least relate in ways that Doyle (being a physician as well as an author), from his perspective and the jargon of his *applied* science background, saw as close enough to describe as "deduction" -- or else on the authorial side just decided that sounded cooler (i.e., rolling off the tongue/page more aproposly story wise or some such), or just what his eccentric character would decide to call it regardless of Bacon et al, etc.
The origins of the words themselves in actual scientific revolution context and the classic/ancient (Latin) roots and prefixes and such are really a kind of meta-authoring emergent thing by peoples and cultures over centuries anyway, so where they overlap (especially between science, medicine, criminal law/criminology etc. as theoretical vs. applied contexts) is probably going to result in some contradictions to begin with. But as long as you consider a more open concept of what language is, as the basis for understanding connections, it seems like there's some interesting basis for what Holmes (Doyle) calls "deduction" and what wikipedia authors clarify as "abduction" being maybe less a continuity error and more illuminating of how different fields may apply the same concepts in different ways (i.e., abstract vs. concrete situations, and other such contrasting aspects).
Or it could be that Doyle was just a physician more than a scientist and, being imperfect and 100+ years before wikipedia made it easier to be sure of most things at least at beginning levels, he goofed.
The former (more complex) possibility is what I deduct/abduct (induct?) so far in as reasonable a way as I can ;-) but I'm sure when I have more time I'll be looking into this further too.