Density refers to the mass of a substance divided by its volume. In soil, we measure density (which we call bulk density) by pounding a cylinder of a known volume into the soil, and then drying the soil for two days in an oven. This gives us the oven dry mass, which we divide by the volume, and thus have the bulk density. There are detailed instructions available for this procedure online at http://soils.usda.gov/sqi/assessment/test_kit.html
In scientific research, this method is used to analyze the effects of different management practices on soil quality, the differences between soil types, and other factors. It can also be used to quantify the differences in soil density at various depths within the soil, which helps in research on soil compaction.
For example, in the graphs shown below, organic matter and bulk density were measured for three depths near the soil surface in a study involving continuous grain sorghum, long-term tillage, and nitrogen rates. In the charts below, CT stands for conventional tillage and NT is no-till; 135 is the amount of N fertilizer applied each year to the grain sorghum, which equates to 120 lbs per acre of actual N. This study ran from 1982 to 2009 with grain sorghum planted every year. It turned out that continuous grain sorghum was not sustainable. Weed pressure eventually caused the end of the study. But the results are still interesting to note. The top 7.5 cm (3 inches) had greater organic matter and was less dense in no-till than in the cultivated soil.
Presley, D.R., A.J. Sindelar, M.E. Buckley, and D. Mengel. 2012. Long-term nitrogen and tillage effects on soil physical properties under continuous grain sorghum. Agron. J. 104:749-755.
DeAnn Presley, Soil Management Specialist