This section is from the book "The Boy Mechanic Vol. 2 1000 Things for Boys to Do", by Popular Mechanics Co.. Also available from Amazon: The Boy Mechanic, Vol2: 1000 Things for Boys to Do.
When the tips slip from shoelaces, new ones may be readily made of fine wire. The wire is run through the end of the lace, Fig. 1, and the two ends are twisted tightly together as shown in Fig. 2. This covers the end of the lace and makes a tip that is easily passed through the eyelets.
Ill: The Wire Prevents the Lace from Raveling and Makes a Tip for Easily Entering the Eyelets