The mine is about half a mile southish of Cairnpapple car park. If you follow the road down where there should be a small sign post marking a foot path to Torphichen. On the east side of the road there should be a gate with a small track, follow that. There you will notice a large body of water and it is on the western bank you will find the entrance its about 1m in diameter. I don't yet know how extensive this mine is yet but hope to find out soon. Another thing, the entrance tunnel joins onto another tunnel after about 30 meters but to reach the end does involve swimming a 5 meter strech and the rest is fairly deep. I hope that helps you wharryburn and have fun exploring.
P.S. Feel free to ask me if you have any problems.