. The gardener's assistant; a practical and scientific exposition of the art of gardening in all its branches. Fig. 912.—Horizontal Training. that the upright is annually stopped so thatone course of horizontals will be made in ayear, then in twelve years, the horizontalsbeing 1 foot apart, the leader will reach thetop of the wall. Presuming that at the expira-tion of this period the lower horizontals of thetrees 1 and 2 meet, it is then evident that onlyhalf of the wall will be covered; for the spacecovered by the side of the tree No. 1, and thatcovered by the side of the tree No. 3, aretoget
. The gardener's assistant; a practical and scientific exposition of the art of gardening in all its branches. Fig. 912.—Horizontal Training. that the upright is annually stopped so thatone course of horizontals will be made in ayear, then in twelve years, the horizontalsbeing 1 foot apart, the leader will reach thetop of the wall. Presuming that at the expira-tion of this period the lower horizontals of thetrees 1 and 2 meet, it is then evident that onlyhalf of the wall will be covered; for the spacecovered by the side of the tree No. 1, and thatcovered by the side of the tree No. 3, aretogether equal to the unoccupied space a be;whilst the space covered by the tree No. 2 isequal to the other unoccupied space cde. Inshort, it is easy to observe that the coveredspaces form four triangles, and that the un-covered spaces form four similar triangles equalto the former, so that half the wall is covered,and half not. Supposing the trees had been planted at halfthe distance apart, as in fig. 913, also that they. Fig. 913.—Horizontal Training. had grown at the same rate as fig. 912, andaccordingly reached the top of the wall intwelve years, it will be observed that at theend of that period all the horizontals, from thebase as far as half the height of the wall, willhave met. The lower half of the wall is there-fore entirely covered, and there is only one-fourth of the surface uncovered. If we cal-culate the difference in regard to time, we shallfind that by planting at half the distance asmuch surface will be covered in three yearsas will be the case in four years by the otherplan. Now, as walls are expensive, it is de-sirable that the whole available space shouldbe utilized. Close planting, as above shown, 49 ai4 THE GARDENERS ASSISTANT. will contribute to that object, and the questionis to what extent this may be carried as regardsthe Pear. In time Pear-trees in good soil willprofitably occupy a wall of ordinary height ifplanted at 30 feet apart; but at such a widedi
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