George Stimpson

It depends on how the fence is built. Suppose a fence is built along one side of a piece of land one mile square. When rolling or mountainous land is surveyed for division purposes it is treated as a plane surface and the surveys are made exactly as if the hills or mountains did not exist. Although there are more actual square rods of surface area in a section of hilly or mountainous land than there are in a section of level land, both contain the same acreage from the surveyor's standpoint. Therefore, in the case supposed, the fence is one mile long regardless of hills and valleys. No more posts or pickets are required to build the fence if the line traverses hills than if it traversed only level land, provided the posts are placed parallel to one another and the same horizontal distance apart. The ground distance between two posts is greater than the horizontal distance and forms the hypotenuse of a right-angled triangle one side of which is equal to the [page 63] round distance between the posts on level land. Accordingly, if only round distance is considered, fewer posts are required to build a mile of fence over a hill than to build a mile of a similar fence on level land, because on the hill the posts are not placed at right angles to the ground. When horizontal distance across the held is considered the number of pots is the same whether the ground is level or hilly. However, when a fence is so constructed it is often necessary to use longer posts on the hillsides, especially if the decline is decided. Sometimes in building fences over rolling ground the posts are set more or less perpendicular to the surface, in which case the posts are not parallel but are slightly closer together at the bottom than at the top. More posts or pickets are required to build such a fence over a hill than to build it on level land. With the wire it is different. In both cases more wire is required to go over a hill because it follows the actual curvature of the ground and a curved line connecting two points is longer than a straight line between the same points.