kantor,
tan delta is a measurement of imperfection of a dielectric medium (ratio of watt losses-imperfection- to var reading-perfect dielectric represented by a capacitor)
just like calculating VAR, W and VA from power triangle, use tangent of angle delta. Assume VAR producing capacitor is parallel with W producing resistor. (in order to find these 3 values, you need to have another reading with tan delta value, VAR value maybe).
divide the calculated total W loss by the volume of the dielectric (assuming uniformity)
hope this helps