We may, however, take the above eleven cases, which are accurate as far as they go, and calculate the weight of the ejected earth which annually flows down a slope having a mean inclination of 9° 26′. This was done by my son George. It has been shown that almost exactly two-thirds of the ejected earth is found below the mouth of the burrow and one-third above it. Now if the two-thirds which is below the hole be divided into two equal parts, the upper half of this two-thirds exactly counterbalances the one-third which is above the hole, so that as far as regards the one-third above and the upper half of the two-thirds below, there is no flow of earth down the hill-side. The earth constituting the lower half of the two-thirds is, however, displaced through distances which are different for every part of it, but which may be represented by the distance between the middle point of the lower half of the two-thirds and the hole. So that the average distance of displacement is a half of the whole length of the worm-casting. Now the average length of ten out of the above eleven castings was 2.03 inches, and half of this we may take as being 1 inch. It may therefore be concluded that one-third of the whole earth brought to the surface was in these cases carried down the slope through 1 inch. {244} It was shown in the third chapter that on Leith Hill Common, dry earth weighing at least 7.453 lbs. was brought up by worms to the surface on a square yard in the course of a year. If a square yard be drawn on a hillside with two of its sides horizontal, then it is clear that only 1/36 part of the earth brought up on that square yard would be near enough to its lower side to cross it, supposing the displacement of the earth to be through one inch. But it appears that only ⅓ of the earth brought up can be considered to flow downwards; hence ⅓ of 1/36 or 1/108 of 7.453 lbs. will cross the lower side of our square yard in a year. Now 1/108 of 7.453 lbs. is 1.1 oz. Therefore 1.1 oz. of dry earth will annually cross each linear yard running horizontally along a slope having the above inclination; or very nearly 7 lbs. will annually cross a horizontal line, 100 yards in length, on a hill-side having this inclination.