The expressions for the variances of the second spatial moments of a solute plume, Varij>, were formulated and evaluated for a line source of finite length either normal or parallel to the uniform mean flow velocity, &mgr;, in a two-dimensional heterogeneous and statistically isotropic aquifer. The evaluations were performed by using the analytical solutions for the velocity covariance derived previously under the first-order approximation to the particle displacement. The main finding is that for the special case of a line source either normal or parallel to the mean flow, not all the variances of the second spatial moments decrease but all the coefficients of variation of the second spatial moments, CVii>, decrease as the initial length of a line source increases. The first-order longitudinal CV11> is independent of the variance of transmissivity, &sgr;Y2, and the transverse CV22> is inversely proportional to &sgr;Y in the case of a line source normal to &mgr;. Comparison between the first-order theoretical results obtained in this study with previous Monte Carlo simulations shows that the match between the theoretical and simulated CV11> improves as &igr;2 increases and in a less heterogeneous aquifer.¿ 1997 American Geophysical Union