here is an intretsing wrinkel, the invisabilty ability of the ring is differant in The Hobbit and the LOTR. in the Hobbit it is made clear that the wearer must becarful because he is not totaly out of site in all light conditions, because though he can't be seen, he will still cast a thin shadow. in the LOTR, this either seems to be forgotten, passed over, or just deemed unimportant in the situations the ring is used. just something to consider.
oh yeah i argee with Eomer, the ring was composed of the power of sauron, it had the abilty to expand and contract at will and " betray it's bearer", it is not out of the range of possabilty that it can decied what "needs" to become invissable with the wearer
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