  I construct multiplicies and orientations of tangent cones to any blow-up set
$Z$ for the Seiberg-Witten equation with multiple spinors. This is used to
prove that $Z$ determines a homology class, which is shown to be equal to the
Poincar\'{e} dual of the first Chern class of the determinant line bundle. I
also obtain a lower bound for the 1-dimensional Hausdorff measure of $Z$.
