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Whip grafting can only be used to join rootstock and scions that are the same diameter, ideally between 1/4 and 1/2 inch in diameter.  The graft must be made after the threat of cold but before the bark of the stock begins slipping (peels off easily). The scion must be dormant (not sprouting) at this time, and should be a twig about a foot long containing three to five buds. Remove the terminal end of the scion. At the base of the scion, make a sloping cut to remove that end. Make a sloping cut across the chosen branch that mirrors the one you made on the scion. They should fit together precisely. Make matching slices down into both the rootstock and the scion in such a way that they can hook into each other. Place the scion slightly offset from the rootstock and slide it down so that the tongues overlap. Make sure that the layer of green wood beneath the bark of both parties aligns or the graft will not take. Wrap a stretchy rubber material around the graft site to hold the scion in place. Grafting tape works well. If using a different material, be sure to remove it in about a month. Once the graft is planted, keep an eye out for new growth below the graft, as you may need to remove it. At first, you can leave some leaves on the rootstock so that nutrients keep flowing up the tree until the graft is successful. However, if you see an actual young branch/shoot forming on the trunk of the rootstock, remove it; this will help encourage the scion to grow. Once the scion really starts to grow and a few new leaves appear above the graft (5 or so healthy leaves), remove any further growths from the rootstock, below the graft. This removal will help the plant thrive with growth on the scion, rather than the rootstock, and has to be done as long as the tree is alive. Otherwise, the rootstock will try to make its own branches; you'll need to remove them whenever they grow.
Choose your cultivar and your rootstock. Prepare the scion. Prepare the rootstock. Cut tongues. Introduce the scion. Secure the scion. Look after the graft.