The numerical solution by McConalogue & Srivastava (1968) of Dean's simplified Navier-Stokes equations for the laminar flow of an inviscid fluid through a tube of circular cross-section of radius a, coiled in a circular arc of radius L, and valid for k in the range (16.6, 77.1), where k = Re $\surd $(a/L), Re the Reynolds number, is compared with experiment, correlated to the asymptotic solutions for k > 100, and extended to study the convective axial dispersion of a substance injected into the tube. The variation of the calculated flux ratio agrees closely with White's (1929) measurements of the inverse quantity over the same range, and the field patterns for the upper end of the range establish the validity of the two basic assumptions of the asymptotic solutions. The original method is extended to calculate the mean axial velocity of a typical particle of the fluid and to present the statistical distribution of mean velocity over the particles of a substance injected as a thin disk uniformly over the cross section of the tube. These distributions are used to display the variation with k of the shape of indicator concentration-time curves. The expected effect of secondary flow, in producing a more uniform distribution of velocity over the fluid than in Poiseuille flow, is evident.