In an ideal world, the bottom of your new Murphy Precision Scope Base, would fit the top of your rifle action perfectly, with no gaps, or misalignment. Unfortunately in the real world, this level of fit isn't likely. Most modern rifle actions are machined to fairly close tolerances, but before the common use of CNC machining equipment, tolerances were much looser. In addition to any errors in the original machining, most rifle actions are polished afterward to remove any tooling marks. While this leaves a pleasing finish, most freehand grinding and buffing can lead to errors of several thousandths of an inch in critical areas. Without bedding, the only solution is to tighten the scope base screws enough to warp the scope base and rifle action sufficiently to make close contact. This warpage can lead to a host of accuracy robbing problems in both your rifle action, and scope.
When properly bedded, high strength epoxy resin fills any small gaps that may exist between rifle action and scope base, allowing full contact with both members in a relaxed state. As an additional benefit, the epoxy resin bonds the scope base the the rifle action, eliminating any recoil stress on the mounting screws.
Before getting anything messy, it is a good idea to dry fit the scope base to your rifle action. Make sure the scope base fits properly with all four provided Torx screws lightly snugged. Do not continue if there are any large gaps, overhangs, or misaligned screw holes.
After you have verified the dry fit of your scope base and rifle action, it is time to prepare the base, screws and action for bedding. First, thoroughly clean the underside of your scope base, and upper surface of your rifle action with an acetone or alcohol soaked rag. Be careful not to touch these surfaces again with your bare hands. Then, apply a liberal coating of release agent or floor polish to the scope base mounting screws. (Failure to follow this step may result in stuck / impossible to remove scope base screws.)
Mix a small amount of epoxy bedding compound according to it's directions, then place all four scope base screws into the scope base to be bedded. Apply a thin layer of bedding compound to the underside of the scope base between and around all mounting screws. (Don't worry about applying too much, as any excess will be cleaned off later.)
Apply scope base with bedding compound to your rifle action, and begin tightening the center two screws until the base appears to be all the way down, and you can just feel the screws begin to tighten. Then tighten the outer two screws until they just make contact.
Wipe off any excess epoxy with rags, then clean up any reside with acetone soaked rags or Q-tips. Epoxy may continue to seep from underneath the scope base for an hour or two, so this step may need to be repeated. Once clean, set action aside for 12-24 Hours to allow epoxy to fully cure and harden. (Consult epoxy manufacturer regarding cure times.)
Once epoxy resin has cured, torque all four mounting screws to the recommended 15 inch-pounds.
That's it! Enjoy your properly bedded scope base.