Mutual Potential of Homogeneous Polyhedra

The mutual gravitational potential between a pair of homogeneous polyhedra is expressed using an infinite series. The nested volume integrals are evaluated analytically and result in simple tensor expressions containing no special functions. However, complexity increases as O(6 ⁿ ), where n is the term degree. An alternate formulation due to Liebenthal is also presented.     

Distribution of forms of sulfur in peats from saline environments in the Florida Everglades

Although there is published information on the mechanism of sedimentary pyrite formation resulting from bacterial reduction of sulfate, little is known about the distribution of forms of sulfur, including organic, in peats. In order to increase understanding of the geochemistry of sulfur in coals, we have determined distributions of forms of sulfur in five cores of saline peat and one of brackish peat, all from areas near the Shark River and Whitewater Bay in the coastal swamps of south Florida. All concentrations vary widely with depth. Total sulfur concentrations range up to 6% of dry solids. Minor amounts of sulfur are present as H₂S, S⁰, SO₄²⁻, and acid-soluble sulfide, but the principal forms are usually pyritic and organic. The ratio, organic/pyritic, is highly variable, but at a majority of levels in a profile is considerably greater than unity. It is inferred that topochemical factors are important in determining the distribution of sulfur forms in any element of volume.