It’s not a matter of geometric proximity. What’s relevant is things like claiming it as your own, attempting to exert control over it, attempting to use its powers, understanding its powers, and so on.
The ring has a malevolent animus all its own. Isildur wore it on his finger and it was still able to betray him. Frodo’s keeping it on his person wasn’t a great idea but it was better than any of the alternatives.
i got the idea that Frodo, through simply having it on his person, was slowly being subjected to the Ring’s influence though he initially had no intention of claiming it. if however, distance was not an issue, then Gandalf would be subject to its influence simply by being in the group, or that Sam would have been the perfect ring bearer instead.
It’s not a case of proximity, it’s a case of ownership. Whether you carry it in your pocket or in your glovebox, the Ring is yours, it’s under your direct control. You can use it any time that you wish. That’s where the temptation comes from. Physical proximity isn’t the issue. Ability to use it is.
Using the Ring, even just wearing it, certainly increases the effects, but aside from that there’s no evidence that physical proximity makes any difference. I guess that in theory if you left it at home and went a hundred miles away, the influence would diminish, simply because your ability to use it is effectively nil.
But once you know, or believe, that it is yours to use, the influence takes hold. That’s why Boromir was influenced simply by being alone with Frodo. He thought he could claim the ring. Galadriel and Gandalf, OTOH, weren’t tempted despite having much more ability to take the ring, because they never saw it as theirs. They only became tempted when Frodo told them they could have it, at which point it effectively came under their control.
This,

… Sauron didn’t care if his Nazgul got the Ring; they were completely domianted by Sauron’s will, and the Ring is really no more than that. Of all the beings in Middle Earth, the Nazgul were completely harmless to Sauron no matter what. …
in the master’s own words,
According to Tolkien’s The Lord of the Rings, the Nazgûl arose as Sauron’s most powerful servants in the Second Age of Middle-earth. They were once mortal Men, three being “great lords” of Númenor. Sauron gave each of them one of nine Rings of Power. … It was Sauron’s design to control all these rings and their bearers through the One Ring, forged in secret for this purpose, but only the Nine succumbed completely to its power and its seduction:Those who used the Nine Rings became mighty in their day, kings, sorcerers, and warriors of old. They obtained glory and great wealth, yet it turned to their undoing. They had, as it seemed, unending life, yet life became unendurable to them. They could walk, if they would, unseen by all eyes in this world beneath the sun, and they could see things in worlds invisible to mortal men; but too often they beheld only the phantoms and delusions of Sauron. And one by one, sooner or later, according to their native strength and to the good or evil of their wills in the beginning, they fell under the thraldom of the ring that they bore and of the domination of the One which was Sauron’s. And they became forever invisible save to him that wore the Ruling Ring, and they entered into the realm of shadows. The Nazgûl were they, the Ringwraiths, the Úlairi, the Enemy’s most terrible servants; darkness went with them, and they cried with the voices of death. — The Silmarillion, “Of the Rings of Power and the Third Age”, 346… In a letter from circa 1963 Tolkien says explicitly that Sauron held the rings:They would have obeyed . . . any minor command of his* that did not interfere with their errand - laid upon them by Sauron, who still through their nine rings (which he held) had primary control of their wills . . . — The Letters of J.R.R. Tolkien, Letter 246
They were by far the most powerful of his servants, and the most suitable for such a mission, since they were entirely enslaved to their Nine Rings, which he now himself held . . . — Unfinished Tales, p. 338
…[RIGHT]CITE[/RIGHT]
*I’m guessing that the “him” referred to here is the Witch-king?
CMC fnord!
Well, the Professor might roll in his grave but I think he’s wrong.
The ruling ring would not tempt the Nazgul. Okay then. Whatever, Professor. Of course, Faramir was too noble to consider it. And Aragorn never really showed signs of being “tempted.”
So everyone from the Maiar to Elves to Boromir. But not the Witch King. Okay then.
If the Witch King truly has no will of his own, he’s less likely to be tempted by the ring than Bill the pony. There would be nothing there for the ring to work on.

So everyone from the Maiar to Elves to Boromir. But not the Witch King. Okay then.
The Nazgul are total slaves to the nine rings, which are held by Sauron. The nine are not wearing their rings at the time LotR is set.

I thought it was Gandalf’s plan to face the Witch King at the gate, but he was pulled away by Denethor’s BBQ?
If I’m not misremembering that bit, why would he have planned to face him if he knew he would lose?
In the book, Denethor asks Gandalf if he is overmatched, and Gandalf replies ‘It might be so’. In other words, it could go either way.

If the Witch King truly has no will of his own, he’s less likely to be tempted by the ring than Bill the pony. There would be nothing there for the ring to work on.
if that is true, then my idea of sending a million homing pigeons* into Mordor might work, amongst them one trained to drop its burden over the lava.
- yeah, yeah. that’s not how homing pigeons work. but in a land of talking trees, the birds will know where to fly!

This,in the master’s own words,*I’m guessing that the “him” referred to here is the Witch-king?
CMC fnord!
The “him” there refers to Frodo- he is discussing what the Nazgul would do if they caught Frodo at Mt. Doom, and if Frodo would be able to command them.

In the book, Denethor asks Gandalf if he is overmatched, and Gandalf replies ‘It might be so’. In other words, it could go either way.
Gandalf’s “It might be so” might also be read as “I’m not going to discuss this with you.” He might have been quite certain in his own mind (either way, and rightly or not), but didn’t want to get into it with Denethor.

Well, the Professor might roll in his grave but I think he’s wrong.
…what? I don’t think it really matters what you think.
The ruling ring would not tempt the Nazgul. Okay then. Whatever, Professor. Of course, Faramir was too noble to consider it. And Aragorn never really showed signs of being “tempted.”
The Nazgul couldn’t be tempted by the Ring. It was Sauron’s will in the Ring and Sauron’s will which completely dominated them. And even if they had it, they still couldn’t beat the Big Bad himself.
Faramir refused it, true. He also wasn’t around it long, nor had (unlike Galadriel) he long stewed over its power and the possibility of saving his people. Aragorn resisted for a while, but he knew he wouldn’t be able to stave it off forever.
So everyone from the Maiar to Elves to Boromir. But not the Witch King. Okay then.
Not exactly. Most people of strong will could have resisted for a while, but their strong will was also their undoing. Once the Ring got its hooks into them, they simply couldn’t let it go. And some beings simply ignored it. Bombadil, for instance, thought it quite absurd: it had no way to get at him, nothing he wanted. Hence, why the Hobbits were so important. They were small, unambitious, but understood the importance of the mission and would never compromise. A man, even the noblest and greatest, would want use the ring to destroy Sauron’s forces. Same for a dwarf, and elf, or even a Maiar.
Well, I apologize for hijacking the thread. Thanks for the responses. I concede the point and figure it won’t be the last time I’m wrong.

The “him” there refers to Frodo- he is discussing what the Nazgul would do if they caught Frodo at Mt. Doom, and if Frodo would be able to command them.
Ahh, I thought “their nine rings” was indicating someone other than the Witch-king, just wasn’t certain.
So, “Yes bearer of The One Ring, whatever your name is, we can stop for burgers . . . but only if there’s a drive-thru and BTW special orders do upset us.”
CMC fnord!
Tolkien also wrote in a letter to a fan that, had Frodo kept the One Ring on his finger and actually spoken to the Ringwraiths, they would have pretended to obey him only long enough to make sure he couldn’t throw the ring into the Cracks of Doom. They would then have taken him to Sauron, who would’ve seized the Ring. Not a word about any of the Ringwraiths being tempted to hang onto the Ring themselves - they were totally in thrall to the Dark Lord.