This Opinion of theirs is founded upon their Notion (which I think very erroneous) of the perpendicular Growth of Vegetables; and is, by Mr. Bradley, set in its best Light, in his Vol. I. Pag. 8. usque ad Pag. 13. and in his Cuts, representing Three Hills; but his Arguments seem to be such as all Arguments are, which pretend to prove a thing to be what it is not; viz. Sophistical ones.
The Hypothesis he endeavours to prove, is in Pag. 8. thus: ‘An Hill may contain Four equal Sides, which meet in a Point at the Top; but the Contents of these Four Sides can produce no more, either of Grain or Trees, than the plain Ground, upon which the Hill stands, or has at its Base: and yet, by the Measure of the Sides, we find twice the Number of Acres, Roods, and Poles, which measure in the Base, or Ground-plat; and therefore Page 9. Hills are worth no more than half their Superficial Measure; i. e. Two Acres upon the Side of the Hill to pay as much as one upon the Plain, provided the Soil of both is equally rich.’
To prove it, he gives an Example in Fig. III. of Buildings upon an Hill; shewing, that the Two Sides of the Hill will only bear the same Number of Houses, that may stand in the Line at the Base.
This is foreign to the Question, of how much Grain, or how many Trees, the Hill will produce. For Vegetables, being fed by the Earth, require much more of its Surface to nourish them, than is necessary for them to stand on; but Buildings require no more of the Surface but Room to stand on: Therefore no such Argument, taken from Buildings, can be applied to Vegetables.
This Argument of Mr. Bradley’s gives no more Satisfaction to the Question about producing of Vegetables, than a Grazier would do, being asked, how many Oxen a certain Pasture-ground would maintain, if he should answer, by satisfying you with the Number of Churches which might stand thereon.
The like Answer, in effect, may be given to the Argument in Fig. IV. of the Pales; only he has forgot to shew, that to mound over the Hill would require double the Rails, or double the Hedge-wood (except Stakes) as to mound the Base; if it did not, the Hill would be yet of the more Value, because thereon more Surface might be fenced in at less Expence.
In his Fig. II. he gives no good Reason why the Hill should not bear twice the Number of Trees as the Base can do; for there is as much Room for Two hundred Trees on the Hill, as for One hundred on the Base, because he allows the Surface to be double to that of the Base. He ought to measure the Distances of the Trees on the Hill, by a Line parallel to the Surface they grow on, as well as he does the Distances of those below.
And suppose the Row at the Base, together with the Surface they grow on, were rais’d up, so that it should become parallel to half the Row on the Hill, would not the Trees in the Base Row be twice as near to one another as the Trees in the Hill Row are? And suppose a Line had been ty’d from the Tops of all the lower Trees, before the Row was so rais’d up at one End, and then, after the Situation of the Row was so alter’d, if by this Line the Trees should be pull’d from being perpendicular to the Surface they grow on, and made to stand oblique to that, and perpendicular to the Horizon, as the upper Trees are; would the Distances of the Trees from one another be alter’d by this Change of Posture? No, for their Bottoms would be at the same Distances, because not removed; and their Tops, because the same Line holds them, at the same Distances in both Postures.
Mr. Bradley’s Lines, drawn from the Trees below, which are one Perch asunder, make the Two Rows of Trees falsly seem to be at equal Distances, because these Lines are parallel to each other: But this is a Deceit; for, in Truth, the Distances of the Trees are not measured by the Distances of those Lines, but by the extreme Points at the Ends of the Lines[222]; and those Two Points above, where the Lines cut the Row obliquely, and at unequal Angles are twice as far asunder as the endmost or extreme Points below are, where the Lines cut the Row at right Angles. Hence may be inferr’d, that there is Room for twice as many Trees to grow on the Hill as on the Base, and twice as much Grain for the same Reason; because there is twice the Surface for the Roots to spread in. And since Mr. Bradley allows the Hill to contain Two Perches to One of the Base, and the Soil of both to be of equal Goodness; and yet affirms, that the Two can produce no more of Grain or Trees than the one Perch can; I cannot see, why it should not be as reasonable to say, that Two Quarters of Oats will maintain an Horse no longer, nor better, than One Quarter of Oats, of equal Goodness, will do.
[222]These upper Trees are measured by the unequal Length of the Lines, not by their parallel Distance, as the lower Trees are; therefore his Measure is a Quibble.