This work investigates the nature of second order effects resulting in solid state nuclear magnetic resonance (NMR), from cross-correlations between the quadrupolar and shielding couplings. Using an average Hamiltonian theory, it is shown that these effects can bring the nonsecular terms of the shielding interaction into the realm of conventional detection. Such terms include the antisymmetric components of the chemical shift tensor, which, although postulated to exist, have hitherto eluded direct experimental measurement. As numerical calculations supported these analytical derivations. an experimental study was undertaken to measure such components from the single-crystal rotation plot of a half-integer quadrupolar nucleus. A custom-made probehead was built, a data analysis procedure developed, and together these were used to analyze the satellite transition spectra arising from a Co-59 single crystal of cobalt (III) tris (acetylacetonate). The results of repetitive studies on such sample are reported.