All kidding aside, the essay in question is “Слов’янські відлуння у творчості Дж.Р.Р. Толкіна” (“Slavic echoes in the works of J.R.R. Tolkien”), by Дмитро Кузьменко (henceforward, Dmitry Kuzmenko). For those who’d like to read it (with or without the help of robots), Kuzmenko has put a copy of the paper up on his website, here. It’s fairly short, a little under 2,000 words, but for those who’d like it even shorter, let me boil down the author’s argument.
Kuzmenko begins with the acknowledgement that Tolkien’s fictive world is one apparently “devoid of any influence of the Slavic culture and especially its literature”, but then asserts that “more detailed analysis shows otherwise” . What does such analysis reveal? Kuzmenko spotlights several pieces of evidence:
- Tolkien’s invented language, Quenya, “has a few Russian words and suffixes”, which probably came about when Tolkien attempted to learn some Russian in 1918 .
- Kuzmenko asserts that “many [of Tolkien’s] toponyms […] were also words of Slavic origin”, such as Rhovanion; or if not necessary given Slavic names, they correspond to Slavic features, as he says the Anduin River springs from the Danube, “which flows mainly among the Slavic peoples and played an important role in their folklore”.
- The example of the wizard Radagast and his home at Rhosgobel, both usually taken to have Slavic sources, although “the exact etymology of the word ‘Radagast’ remains controversial”; it is here that Kuzmenko cites me, specifically this post written for Lingwë.
- The Variags of Khand, who (it can scarcely be argued) take their name from the Varangians, Norsemen who settled in the regions we now call Russia, Belarus, and the Ukraine.
- The original name for the character who would become Beorn in The Hobbit: Medwed, a Slavic name with the meaning “bear, honey-eater” (and which I also discuss at some length in the post on Radagast).
- Kuzmenko suggests that “several images [...] at first glance have a Germanic origin, but on closer examination reveal Slavic parallels”, and discusses three: Mirkwood, Wargs, and the dragon Smaug.
Kuzmenko’s essay therefore doesn’t break new ground, which unfortunately tends to undermine its mission of convincing us that Slavic elements in Tolkien’s writings deserve greater attention and investigation. Tolkien himself would seem to discourage the mission, having said that “Slavonic languages are for me almost in the same category [i.e., no aptitude]. I have had a go at many tongues in my time, but [...] the time I once spent on trying to learn Serbian and Russian have left me with no practical results, only a strong impression of the structure and word-aesthetic” .
There is a problem inherent in arguments like those of Orr and Kuzmenko; actually a couple of problems. For one, the mere existence of Slavic cognates to Germanic words we know were of interest to Tolkien says nothing about whether Tolkien was or was not aware of them, let alone whether he intended them to be detectable by readers (with one exception: “Variag”). For another, we often don’t know which cognates were the older ones, the Germanic of Slavic, though in some cases — as of, say, Gothic versus Old Church Slavonic — it’s pretty clearly apparent which is older. Third, even if a Slavic form is older and was borrowed into Germanic, we have no reason to assume either that Tolkien knew this, or that he cared if he did know. And if we are only interested in cognates, why not trot out a whole wealth of Sanskrit words? Why not? Because there is absolutely no evidence that Tolkien had Sanskrit in mind at any stage of the development of Middle-earth. One can make almost as definitive a rejection of the Balto-Slavic branch — but instead of absolutely no evidence, it’s rather simply very little. Certainly much less even than the Goidelic branch of the Celtic family, which Tolkien himself largely rejected.
For one example of something that has been made too much of, take Medwed, the original name for Beorn. Yes, this name is incontrovertibly Slavic. But why should this be cause for Slavists to rejoice? Tolkien rejected the name before publication of The Hobbit, replacing the Slavic name with a Germanic one. The fact of that rejection says something about Tolkien’s attitude toward the suitability of Slavic elements in Middle-earth, and should probably discourage the overenthusiastic search for others.
Note that I don’t mean to discourage all research in this area — far from it; I’m thinking only of the really overzealous, “no stone unturned” searches. As I indicated above, there is one very clear exception case, in Variag. This form, retained in the final published Lord of the Rings, is undeniably Slavic, from the Russian варяг, in turn from Old East Slavic (i.e., Old Russian, sometimes called Old Ukrainian) varęgŭ. The word is still in use today, actually. In Belarussian, as I understand it, вараг means both Varangian, but also (colloquially) any “tall, burly man”, and in the Arkhangelsk dialect of Russian, варяза is used to mean “a man from beyond the sea, a foreigner” (this is almost exactly, but coincidentally, analogous to the Semitic ferengi, which I have discussed before).
But aha! Despite the clearly Slavic word-shape Tolkien chose, its source is ultimately Germanic. Cognates include Old English wǽrgenga, Lombardic waregang, Old Frankish wargengus, cf. medieval Greek βαράγγως — all ultimately sourced to Old Norse væringi, váringi, from Proto- Norse *váringr, believed to derive from vár “vow, oath, pledge” + ganga “to go”, in the sense of foreigners pledged to service.  The word isn’t attested in Gothic, but if the Goths used the word, it would most likely have taken the form *wadjagagga, from wadi “pledge” + gagga “to go” (cf. the genuine faúragagga “a steward, lit. fore-goer”). The point is that although Tolkien chose a Slavic form for its presentation in the Middle-earth of the Third Age, the word, the very idea, of the Variags has its roots in Scandinavia, much as Beowulf has roots in Scandinavia but is seen through a distinctly English lens. And whatever (few) other Slavic echoes one might detect in Tolkien’s legendarium should, I expect, be regarded in the same way.
 Kuzmenko, Dmitry. “Slavic Echoes in the Works of J.R.R. Tolkien.” Literary Studies (National University of Kiev) 24 (2009): 217–221. All quotations are in English, machine-translated, then edited for sense by me. If you speak Ukrainian, please feel free to suggest corrections.
 Kuzmenko gives no source for the claim that Russian left an imprint on Quenya; however, he must have gotten this from Ivan Derzhanski’s entry, “Russian Language”, in Michael Drout’s Tolkien Encyclopedia (pp. 581–2). Kuzmenko includes Drout as an entirely generic entry in his bibliography, but does not explicitly cite it in the essay.
 Orr, Robert. “Some Slavic Echoes in J.R.R. Tolkien’s Middle-earth.” Germano-Slavica 8 (1994): 23–34. This is a solid essay, worth reading, but I think Kuzmenko may have relied rather too heavily on it. Kuzmenko’s assertion that “several images [...] at first glance have a Germanic origin, but on closer examination reveal Slavic parallels” is uncomfortably similar to Robert Orr’s “elements which at first appear to be simply taken from Germanic, but which on closer inspection appear to have various sorts of Slavic associations” (p. 23). Moreover, the three examples Kuzmenko gives — Mirkwood, Warg, and Smaug — are the same three Orr discusses, in the same order.
 Tolkien, J.R.R. The Letters of J.R.R. Tolkien. Ed. Humphrey Carpenter. Boston: Houghton Mifflin, 1981, p. 173 (#142).
 Blöndal, Sigfús. The Varangians of Byzantium. Trans, rev., and rewritten (!) by Benedikt S. Benedikz. Cambridge: Cambridge University Press, 1978. Reprinted 1981, 2007. pp. 4–6.