Yes, yet another LOTR question!!
As far as I understand, the ring wraiths can tell when they are getting close to the ring… sort of a “it’s getting hotter… hotter… oops colder, wrong direction” thing.
Why then, when they seem to be in very close proximety to the ring, do they look briefly around and then run off looking elsewhere? Wouldn’t it seem like a good idea to do a more detailed search of the area?
I think the idea is, they can’t sense the Ring unless it’s being worn. Their presence is detected by the Ring, though, and it tries to influence its bearer to put it on, so the Ringwraiths can see him or her. The Ringwraiths can’t really see anything in our world, so they rely on their hearing and smell, and the sight of their mounts to guide them. Once the Ring is worn, the bearer is brought into the spirit-world the Nazgul exist in, and is completely visible to them.
I believe the idea was that if the Nazgul got close enough, the RING was supposed to seduce its bearer into putting the thing on, or at least making some kind of screwup to reveal his presence…