Can you identify this Rolex?

[Johnathan Sussex]

Okay, i am posting this here aswell in hope that somone with some knowledge about early models will be able to help me!

A few years ago, a friend of my mother gave me her grandfather's old Rolex, the bracelet part was brown leather and the watch itself looked like a Prince. The Rim was made of gold and behind the glass, the watch (Please excuse my english) was black and the word ROLEX was on it. I don't think there is any serial number on the back, it could be one of the very early rolex watches. Can anyone try to guess with me which Rolex it could be and how much it is worth? Even though it seems in a perfect state it is way too old and unless i constantly shake my hands (one firm shake every 6 hours) it stops running or indicates the wrong time. It has allready been serviced several times (That did cost me a fortune!) and even though it is a very nice watch i think i would like to sell it some day and buy another Rolex which will be less fragile (Yes! I do get nervous when i wear my old Rolex. In fact i only wear it for formal occasions, i wish i had a nice watch which i could wear all the time) and which works better. I do know that it is authentic (I asked a jeweler and he said that it indeed seemed to be gold).