  We present a new method of measuring the mass density along the line of
sight, based on precise measurements of the variations of the times of arrival
(TOA's) of electromagnetic signals propagating between two distant regions of
spacetime. The TOA variations are measured between a number of slightly
displaced pairs of points from the two regions. These variations are due to the
nonrelativistic geometric effects (Roemer delays and finite distance effects)
as well as the gravitational effects in the light propagation (gravitational
ray bending and Shapiro delays). We show that from a sufficiently broad sample
of TOA measurements we can determine two scalars quantifying the impact of the
spacetime curvature on the light propagation, directly related to the first two
moments of the mass density distribution along the line of sight. The values of
the scalars are independent of the angular positions or the states of motion of
the two clock ensembles we use for the measurement and free from any influence
of masses off the line of sight. These properties can make the mass density
measurements very robust. The downside of the method is the need for extremely
precise signal timing.
