Limitations on the additivity of moments in line‐profile analysis

The leading terms in the centroid‐range and the variance‐range curves are additive in the contributions made by the various sources of line displacement and line broadening. The intercept of the variance‐range curve contains non‐additive contributions inherent in the slow approach to zero of the functions convoluted in the line profile. Further terms in the series for these curves contain non‐additive contributions that depend both on the functions convoluted and the range used; these terms approach zero as an inverse power of the range as this is increased.