The properties of the magnetic variance matrix M in the context of remote sensing of two-dimensional (2-D) coherent flux transfer events and waves on the magnetopause or other current sheets are investigated. It is known from previous work that, in theory, the smallest eigenvalue of M should be zero and that the corresponding eigenvector should lie in the plane tangent to the unperturbed current layer, forming a certain, theoretically predictable angle, &thgr;N, with the invariant direction (or axis) of the event. For a certain class of events, we now demonstrate the following additional properties: (1) The direction of the vector normal to the unperturbed current layer should coincide with either the maximum or the intermediate variance eigenvector, depending on the Mach numbers of the plasma; and (2) the ratio of maximum to intermediate eigenvalue of M is related in a simple manner to the so-called stretching factor R and to the angle &thgr;N, permitting both to be determined without use of the Hilbert-transform fitting technique and the trial-and-error approach to finding &thgr;N previously employed [Walthour et al., 1993>. Magnetopause events from the spacecraft AMPTE/CCE, AMPTE/IRM, and ISEE are used to illustrate the new results. ¿ 1998 American Geophysical Union