For the analytical and numerical description of the emittance of a particle beam in cylindrical symmetric transport and accelerator systems often therr′plane is used, yielding a sectional emittance&egr; (r, r′).In contrast, emittance measurements are mostly taken as the projectional emittance&egr; (x, x′).As could be shown earlier, the description of a cylindrical symmetric beam in the projectionalxx′plane of phase space results in the presence of lines for each ring of particles, connecting the two corresponding points, with which the same beam is described in therr′plane. There is a very special intensity distribution along these lines, both for straight as well as for skew trajectories. It is shown here that the theoretically obtained density distribution along such a line is a weight function for the intensity measured with a slit of width&Dgr;x.For one particle it can also be interpreted as a probability function for the particle being at a certain positionx0.In view of Liouville’s theorem, the case of the two-dimensional emittance in cylindrical symmetric systems is discussed, where this law of conservation is, due to the coupling of thexandyplanes, not generally applicable. It is shown here that for an emittance measurement performed in thexx′plane, care has to be taken when choosing the slit width, since a small&Dgr;xyields a good spatial resolution, but increases the risk of missing information in the center of each connecting line. ©1997 American Institute of Physics.