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.
The trick of changing a rubber band from the first and second fingers to the third and fourth, if done quickly, can be performed without detection by any one. The band on the first two fingers is shown to the spectator as in Fig. 1, with the back of the hand up. The hand is then turned over and the band drawn out quickly, as shown in Fig. 2, in a manner as to give the impression that the band is whole and on the two fingers. While doing this, quickly fold all the fingers so that their ends enter the band, and turn the hand over and let go the band, then show the back with the fingers doubled up. In reality the fingers will be in the band, as in Fig. 3, and the back will still show the band on the first two fingers. Quickly straighten out all the fingers, and the band will snap over the last two fingers, as shown in Fig. 4. - Contributed by E. K. Marshall, Oak Park, Ill.
Ill: Transferring Rubber Band from the First Two Fingers to the Last Pair, Like Magic