_Air-space in Natural Soils._—The difference between the specific gravity as usually determined, and the volume-weight of soils, is of course caused by the large amount of air contained in them when dry, but which in wetting them is partially or wholly replaced by water. [Illustration: FIG. 10.—Various possible arrangements of soil particles.] Theoretically, assuming all soil grains to be globular, and packed as closely as possible (in oblique order), the space not filled by them would be the same for all sizes, whether that of marbles, or so minute as to be hardly felt between the fingers; and would be 25.95 per cent of the soil volume.[30] If the same globular particles were packed as loosely as possible, _i. e._, in square instead of oblique order (see figures 10 and 11), the vacant space would be 47.64 per cent If however we imagine each sphere to be itself composed of a number of smaller ones, the empty space will obviously be greatly increased, to an extent proportionate to the diminution of solid mass thus brought about. The pore-space might in that case, with the oblique arrangement of the globules as shown in Fig. 10, be as high as 74.05 per cent But since the soil particles may be of all shapes and sizes within the same soil, and usually fit much more closely than would globular grains, the empty space rarely approaches (only in certain alluvial soils and in loose mulches) to the figure last named. In sandy soils it may fall as low as 20%, and in coarse gravelly soils even as low as 10%. Most cultivated soils range between 35 and 50% of empty space. [30] King, Physics of Agriculture, p. 116, ff. _Effects of Tillage._—That these figures can be only approximations is obvious from the consideration that one and the same soil will vary materially in its volume-weight according to its temporary condition of greater or less compactness. After land has been beaten by winter rains, its volume-weight will be found to have materially increased from the well-tilled condition brought about by thorough cultivation. This difference is strikingly seen when, in plowing, the height of the ground on the land side is compared with that of the turned furrow-slice in well conditioned loamy land. This loose condition is called _tilth_, and it results from the formation of relatively large, complex crumbs[31] or floccules, between which there are large air spaces that were wholly absent in the untilled land; the floccules themselves being also more loosely aggregated than was the case before tillage. [31] The word crumbs, which is generally understood as meaning a relatively large, loose aggregate, seems preferable to the word kernels, suggested for the same by King (Physics of the Soil, p. 110). Kernels are understood to be bodies rather more solid than the surrounding mass, and do not convey the idea of loose aggregates. The word “Krümelstructur” (crumb-structure), adopted by Wollny for this phenomenon, has both fitness and priority in its favor.