Is publically a word? Yes, if by “a word” you mean “a term that is found as an entry in dictionaries.” But is it a word a careful writer is apt to use? That’s another story, which will be told below.
First, dictionaries are not arbiters of highly literate writing; they merely document usage. For example, irregardless has an entry in many dictionaries, even though any self-respecting writer will avoid using it—except, perhaps, in dialogue to signal that a speaker uses nonstandard language, because that is exactly how some dictionaries characterize the word. Yes, it has a place in dictionaries; regardless of that fact, its superfluous prefix renders it an improper term.
But what about publically? Let’s examine this word more closely: It’s an adverb, which is a part of speech that modifies a verb or any one of various other parts of speech. Usually, an adverb is employed to further explain the way something is or how it occurs, as in “oddly shaped table,” where oddly provides more information about how a table is shaped. Publically, similarly, serves the role of modifying an adjective that modifies a noun, as in “publically available information.”
The problem with that phrase, however, is that publically is nonstandard. That is, it is common, but not considered correct: The proper form is publicly.
You may think that word looks odd, as if it has been rear-ended and a couple of parts (namely, an a and an l) were left behind at the scene. But most adverbs are simply adjectives with an -ly ending attached, and the adjective public (as in “public property”) has been so transformed.
But wait, you might say, what about all the other adjectives ending in -ic that are converted into adverbs by adding -ally rather than simply -ly: logically, radically, and statistically, for example? Well, for one thing, in each of those words, -ic is a common element, but in public, the pertinent component is -lic. For another thing, the adjectives on which these terms are based end not in -ic but in -al: logical, and so on. (However, some adverbs that end in -ic, without the additional -al syllable, such as basic, acquire an -ally adverbial ending rather than simply -ly.)
So, some adjectives become adverbs by attaching -ally, but public is not one of them, at least as far as careful writers are concerned.
Why is it, then, that although publicly is far more common as the adverbial form of public than publically, the ratio of usage has diminished? Publically is becoming more common for the same reason that people write irregardless in place of regardless or write “diffuse the situation” instead of “defuse the situation” or “all of the sudden” rather than “all of a sudden”: evolution.
Language is, in a sense, alive, and just as life itself evolves, so does language—but note that the primary definition of evolution is not “improvement”; it simply means “change.” And how does language change? The change is modeled: New words are coined, or new senses of existing words develop (or new spellings or new forms occur), because someone, somewhere acts to make it so, and the evolution goes viral.
Several factors are at play in the evolution of written prose: First, education in grammar, usage, and spelling has declined. Second, a smaller proportion of the population than before reads authoritative, carefully written prose, whether exemplary fiction and nonfiction literature in book form or high-quality journalism in periodical form, and because of a pervasive decline in quality control, even professional publications are more likely than in the past to contain errors. Third, publishing has become more pervasive—virtually anyone can publish a book or a blog, and many people who do so are not vigilant about maintaining high writing standards.
In the case of publically, therefore, the decline in the kind of rigorous instruction that inculcates proper writing style allows nonstandard spelling to flourish, professional publishers of periodicals and books (and web sites) allow such errors because even some professional writers (and editors) suffer from instructional neglect and many companies employ too few, if any, copy editors and proofreaders, and many amateur publishers are ignorant of or indifferent about these kinds of errors. As a result, consumers of print and online publications ingest and regurgitate such errors, perpetuating and propagating them. (There is also the factor of obsolescent idiom: If you don’t know, for example, that deserts is a formerly common but now rare word meaning “what is deserved,” you’re likely, when you intend to refer to the old-fashioned idiom “just deserts,” to spell the second word desserts because of your misapprehension that the phrase refers ironically to a sweet dish served after a meal.)
Change happens—but although we must accept that may be inevitable, we don’t have to enable the change or encourage its acceleration; it will happen on its own without our assistance. In the meantime, we can decide to be careful writers who consult authoritative sources that will assist us in crafting clear, concise, correct prose (for example, by avoiding using words labeled in dictionaries as variants—and not being one of those people who say, “Well, I’m still going to spell it publically”). I publicly (not publically) rest my case.