These observations led me to make others with more care.Eight castings were found on my lawn, where the grass-blades are fine and close together, and three others on a field with coarse grass.The inclination of the surface at the eleven places where these castings were collected varied between 4 degrees 30 seconds and 17 degrees 30 seconds; the mean of the eleven inclinations being 9 degrees 26 seconds.The length of the castings in the direction of the slope was first measured with as much accuracy as their irregularities would permit.It was found possible to make these measurements within about of an inch, but one of the castings was too irregular to admit of measurement.The average length in the direction of the slope of the remaining ten castings was 2.03 inches.The castings were then divided with a knife into two parts along a horizontal line passing through the mouth of the burrow, which was discovered by slicing off theturf; and all the ejected earth was separately collected, namely, the part above the hole and the part below.Afterwards these two parts were weighed.In every case there was much more earth below than above; the mean weight of that above being 103 grains, and of that below 205 grains; so that the latter was very nearly double the former.As on level ground castings are commonly thrown up almost equally round the mouths of the burrows, this difference in weight indicates the amount of ejected earth which had flowed down the slope.But very many more observations would be requisite to arrive at any general result; for the nature of the vegetation and other accidental circumstances, such as the heaviness of the rain, the direction and force of the wind, &c., appear to be more important in determining the quantity of the earth which flows down a slope than its angle.Thus with four castings on my lawn (included in the above eleven) where the mean slope was 7 degrees 19 seconds, the difference in the amount of earth above and below the burrows was greater than with three other castings on the same lawn where the mean slope was 12 degrees 5 seconds.
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 degrees 26 seconds.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 wholeearth brought to the surface was in these cases carried down the slope through 1 inch.
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 of the earth brought up can be considered to flow downwards; hence 1/3 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.
A more accurate, though still very rough, calculation can be made of the bulk of earth, which in its natural damp state annually flows down the same slope over a yard-line drawn horizontally across it.From the several cases given in the third chapter, it is known that the castings annually brought to the surface on a square yard, if uniformly spread out would form a layer 0.2 of an inch in thickness: it therefore follows by a calculation similar to the one already given, that 1/3 of 0.2x36, or 2.4 cubic inches of damp earth will annually cross a horizontal line one yard in length on a hillside with the above inclination.This bulk of damp castings was found to weigh 1.85 oz.Therefore 11.56 lbs.of damp earth, instead of 7 lbs.of dry earth as by the former calculation, would annually cross a line 100 yards in length on our inclined surface.