Join Date: Nov 2007
Location: SF Bay area
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Fundamentally, your spring lines keep you from drifting foreward or backward at the dock, so they run at a shallow angle from the boat to the dock. Usually you have two at the midships cleat, one running forward (the forward spring) and one running aft (the after spring).
However, some people don't have a midships cleat, so they run a line forward from the quarter cleat (the forward spring) and back from the bow cleat (the after spring). In other words, the line is named by the direction it runs, not the position of its boat-end. They can be called "bow spring" and "quarter spring as well" if you need to specify where they are tied to the boat.
As for how you tie it, there are a few methods. You can put a half-hitch on the cleat (i.e. the free end goes under the standing end), or if you have an eye (loop), you can put the eye between the cleat's "legs" and then over both horns. For fast-removing but less secure hold, you can (on an after spring) put the eye over the after horn, then run the line around the forward horn, inboard to outboard, and then aft.
Again, spring lines are primarily for preventing fore-and-aft motion of the boat. Spring lines don't do much to prevent rolling or pitching of the boat, since those actions don't require the lines to stretch very much (mostly just change their angle to the dock slightly). They may help a bit with yawing, but if you have brest lines on (the lines that run more or less perpendicular from bow and stern to dock), that will do much more to prevent yaw.
One thing you might try to dampen rolling a bit is to run a line from the stern cleat that's not next to the dock at about a 45-degree angle to the dock. You might be able to use your "port stern" cleat for that. Another thing you could do is snug the boat a bit tighter to the dock.
Some more information would be helpful: what sort of a boat have you got? (hint: put it in your signature!) What is it tied to? (options are: pier on pylons, floating platform, seawall). If it's a floating platform, how is the platform secured? What have you got near you besides the "dock" itself? Some slips have freestanding pylons you can throw a loop over, for example.
Lastly, photos would be great.