This section is from the book "The Gardener V3", by William Thomson. Also available from Amazon: The New Organic Grower: A Master's Manual of Tools and Techniques for the Home and Market Gardener.
To perform the operation of whip or tongue grafting, first cut over the stock to the required height; then, with a sharp thin-bladed knife, cut a slice 3 inches long off the stock, as represented at a of our woodcut. This cut should be clean and smoothly made, and with one pull of the knife. Cut a thin tongue, about half an inch long, half-way down the cut. Make the bottom end of the scion or graft b in the very same way; only let the tongue be cut upwards instead of downwards, as in the stock. Then place the graft on the stocks, inserting the one tongue into the other, as represented at c. Secure the union firmly with matting, and apply the grafting clay. Be careful that the edges of the bark of the scion and stock are nicely fitted, so that they meet exactly at both sides. This is the method generally used when scion and stock are of equal diameter; and when they are not so, and the bark cannot be adjusted on both sides, then they must be united at one side. Crown-grafting, as represented in engraving, is generally practised when old trees are headed down and grafted with young shoots. The scion, as you will observe, is prepared in the same way as in whip or tongue grafting, minus the tongue; and it is inserted between the bark and wood of stock.
It is often necessary in the case of old trees to "slit" the bark perpendicularly, in order to get the bark to rise sufficiently to admit the scion, which requires to be inserted far enough to let its shoulder rest on the top of the stock, Shield-budding is the method most suitable for budding Cherries and Plums, and in the case of standard trees they are budded, but very dwarf trees are more frequently grafted. The engraving will explain to you the operation of shield-budding.
Fig. 9. "Whip or Tongue Grafting.
Fig. 10. Crown-Grafting.
Fig. 11. Shield-Budding the Rose.