This section is from the book "The American Garden Vol. XI", by L. H. Bailey. Also available from Amazon: American Horticultural Society A to Z Encyclopedia of Garden Plants.
Although the practice of budding young seedlings of the peach and some other fruits in the early part of the first summer has been carried on for more than fifteen years, it is yet comparatively a new thing. The objects to be gained are the production of a budded tree the first year, thus saving the expense of one year's growth in the nursery ; the advantage of transporting a small tree instead of a large one; and enabling the nurserymen to dig the trees with a larger proportion of root, thus lessening the danger of loss in transplanting. The peach is perhaps the most easily operated upon of any of the fruits, as the seedlings grow very rapidly and make a stock sufficiently large to insert buds upon in time for them to grow and mature healthy wood before fall.
Although the term "June budding" is commonly used, my experience has led me to think it should be more properly called "July budding," as nearly all my successful experiments have been made in Kansas during the early part of the latter month.
The process is indeed very simple, as all that is required is a healthy, vigorous stock and buds which are sufficiently developed to grow after having been inserted. This, of course, must be left to the discretion of the operator, and "bud sticks" will have to be taken, of which a large portion of the tip end will have to be cut off as too tender or immature.
The buds are inserted in the usual manner, but the wrapping should be of some rather elastic material which will readily yield to the rapid growth of the tender stock. I have found strips of old muslin very good, although I have used bass-wood bark with a reasonable degree of success. As soon as the buds are set the top of the tree should be cut back severely, or the stem cut partly off about four inches above the bud, and bent over in order to check the growth of the top and force the bud into growth. If the stock is cut off immediately, the remaining part is liable to die. As soon as the bud has grown a few inches in length the entire top may be cut away close to the shoot.
Washington. H. E. Van Deman.

Fig. 5. Stock cut back, and tie removed, to start bud.
 
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