s-Hausdorff measure of Cantor set

If s = ln(2)/ln(3) (the Hausdorff dimension of the Cantor set), what is the numerical value of the s-Hausdorff measure of the Cantor (ternary) set, and how does one calculate it? Is there a general method? I know that it equals the limit as d goes to zero of the sum of (diameters to the s-th power) of the sets in a d-cover of the Cantor set, but this doesn't help me actually calculate a specific number. I know there is a formula for a "ball" in any given dimension, but that doesn't help either. (Doh)