Below, a simple splice is illustrated on 1/8" single braid spectra rope. There are other, more complicated but secure methods of eye splices. Some will not allow splicing of both ends of the rope as this example does. Whipping of the splice is required to ensure that the splice doesn't work its way out.
Sharp scissors, razor blade or knife
Fid: solid rod of appropriate diameter and length ( 3/32" Ti rod used in example)
Fiber tape: cut width wise to allow for overlapping circumference of rope
Step 1: Lay Rope and Fid Longitudinally at One Side of Fiber Tape. Allow a Gap Between Ends.
Step 2: Oll Fid and Rope Up in Fiber Tape
Step 3: Open Weave of Rope and Push Fid Through From One Side Through the Other
Step 4: Pass Fid Through Rope Again From the Other Side
Step 5: Open Weave of Rope on One Side, Close to Where the Fid Tail Has Come Through. Carefully Feed Fid Down Interior of Rope for a Few Inches and Then Let Fid Exit Center of Rope.
Step 6: Pull Fid Tail Until Eye Remains and the Section of Rope Covering the Tail Is Bunched
Step 7: Cut Fid Tail and Stagger Lengths of Individual Strands of Tail. This Allows for a Smooth Taper in Splice
Step 8: Milk Cover Over Tail Until Tail Disappears Into Rope and Rope and Splice Are Tight
Step 9: Use Waxed Whipping Twine to Set Splice. Notice Tail of Twine at Left and Loop at Right
Step 10: Tightly Wind Twine Around Splice Working Towards Loop (from Left to Right)
Step 11: When Sufficient Whipping Is in Place to Cover Splice, Cut the Twine Free From the Spool Leaving About 6" of a Tail. Feed This New Tail Through the Loop at Right.
Step 12: While Holding the Tail at Right, Pull the Tail on the Left Until the Loop Disappears Under the Whipping Coil and Is Pulled Almost All the Way Through. in Photo Above the Loop Has Yet to Disappear.
Step 13: The Loop Is Now Inside the Whipping Coil. by Pulling Tightly on Both Tails, the Whipping Coil Gets Tighter on the Rope Splice As Well As on the Tails. Keep the Loop Centered Under the Coil (from Left to Right)
Step 14: Cut Tails of Whipping Close to the Whipping Coil. This Whipping Is Completed, But in This Example, the Whipping Doesn't Cover the Splice Nicely - DUH!! (For Ease of Photography Proper Placement of Whipping Was Ignored)
Step 15: In This Photo, Whipping Was Redone, With Proper Placement Over Splice in Rope