That's what I was wondering. Perhaps magic, if they couldn't climb up or down it had to have been magic.
Maybe they had very, very, very good aim and were able to throw rocks well enough to carve-Nope.
I don't know! I came accross that, too, but I guess I let it slide for a while. Good topic!

Well, the text doesn't really say that the ring caught on a rock near the inscription, though it also doesn't say it didn't. What it says is, "Up went the ring, flashing in the sunlight, and caught, and hung, as neatly as a well-thrown quoit, on a little projection on the rock." Then again, the illustration seems to show it hanging beside the words, so I don't know. Maybe they were just making an excuse not to get it because no one wanted it. Or it might just be magic or have no explanation at all. Maybe we'll never know.

I always assumed that the words were carved lower than the ring. They carved the words before they knew what was going to happen to the arm ring, so it would make sense that they carved them without any consideration as to where the projection was. They probably carved the inscription as high as they could reach so it would be easily visible. I wonder how high Caspian threw the ring.

Then again, the illustration seems to show it hanging beside the words, so I don't know.

This wouldn't be the first time an illustration was wrong. In the color versions, Susan has blond hair some of the time instead of dark hair and Lucy has dark hair some of the time instead of blond hair.

The words most definitely would have been carved lower than the ring. If they were carved half-way up the cliff than:

A: Somebody would have had to climb up there in order to etch them.

B: The lettering would have had to have been huge in order to read from the ground.

Baynes got the illustration wrong. As Patertwig's Pal pointed out, Baynes also drew Lucy with dark hair, when the books clearly state that she has blonde hair. Susan however, who has dark hair, has blonde hair (at least in HAHB).

Maybe the words were carved somewhere that could be reached but the arm ring landed somewhere that couldn't, maybe on top of a steep cliff with no hand or foot holes to climb with. Besides I don't think the book says how high the words were written, maybe just as high as the could reach from the ground, if the ring was thrown much higher it's not so far-fetched to think that no one would be able (or willing) to climb for it.

I agree that they might have been able to reach where the words were, but not the little bit higher to where the arm ring was. I think that could easily be possible.

Also the original drawings were not in color. They were black and white.

I agree that they might have been able to reach where the words were, but not the little bit higher to where the arm ring was. I think that could easily be possible.

A good point, but for anyone to read the letters from the bay, they would have to have been carved pretty large and fairly high up. For the arm ring to be up higher than that means that Caspian would have super-human throwing ability.
(If he did have that good a throwing arm, the NFL draft would have found out and gotten him a contract, so that's not the answer, jk)

Probably the only way the inscription could have been written is, as was said before, by writing it much lower than where the ring was hung. In a lot of C.S. Lewis books, they'll state how he and Miss. Baynes only met once before he hired her, and then just sent her the story so that she could illustrate it supposedly because he felt uncomfortable around her. That would explain the small amount of interaction except for phone conversations when there was something he wanted to be exact. As far as him knowing what the pictures looked like, he either didn't notice this when he reviewed them, or didn't think it really mattered. Either way, the inscription was written and the ring was caught onto someplace near it.

I have always wondered this ever since I first read the book. It makes no sense to me.

I have seen no illustration for this scene but I find no difficulty in imagining it.
We’re told that Caspian

... caused [the words] to be cut on a smooth cliff facing the bay ...

Clearly, then, one or more of the Dawn Treader’s crew inscribed the words, with no need for magic, using ordinary tools which were already part of the ship’s equipment. We may safely imagine that each letter of the word was over a few centimeters in height (for otherwise it would be too difficult a task for presumably inexpert monumental masons to inscribe legibly) yet no larger than a handspan or so.
We may imagine that there was a sandy or rocky section of beach, with scree, or perhaps even a pleasant stretch of greensward, between the cliff and the bay because

they were all standing looking at the inscription.

We are not told how high the smooth cliff was but, assuming that it was twenty meters high, one can easily consider that it was so smooth, and, by definition, nearly vertical (and perhaps even looming over the ship’s complement) that it would have been virtually impossible for any but the most experienced rock climber to ascend even with the aid of ropes.
King Caspian, being a fit young man, could have easily tossed the ring vertically ten or so meters; the ring, at the vertex of the throw, when it had minimal acceleration, then landed “on a little projection” of the otherwise sheer rock-face, and stayed thereon.
A particularly determined crewman, no doubt, could have gone to some trouble to gather some ship’s lines and to rappel to the ring but, since Eustace, Caspian and Lucy declined to keep it, we may safely assume that no one else really felt inclined to collect it.
So, one may imagine a section of sheer cliff of more than twenty meters in height, close to a bay, featuring an inscription, of as much as one square meter in size, with the top thereof being about one and a half meters above the fairly flat ground at the cliff’s base base; and, say, seven or eight meters above the inscription, a gleaming bracelet can just be discerned on a slight projection of the rock-face.

In the book I have, there's a picture that shows the arm band hanging within six inches of the inscription.

This never occurred to me. I didn't even notice it when reading the book!!! I'm not sure how they etched it there, and we may never know! Maybe it was magic, or perhaps it was farther down. If the illustration was wrong, as some of you have said, it wouldn't be the 1st time. Who knows?

How can we possibly know that it is within six inches? There is no reference in the picture at all. The letters may each be six feet tall so they can be read from afar. It is quite possible that they could reach there and are not able to reach the last few feet to where the ring landed.