A Note on $4$-Rank Densities For certain real quadratic number fields, we prove density results concerning $4$-ranks of tame kernels. We also discuss a relationship between $4$-ranks of tame kernels and %% $4$-class ranks of narrow ideal class groups. Additionally, we give a product formula for a local Hilbert symbol. Categories:11R70, 19F99, 11R11, 11R45