  The so-called Limber equation is widely used in the literature to relate the
projected angular clustering of galaxies to the spatial clustering of galaxies
in an approximate way. This paper gives estimates of where the regime of
applicability of Limber's equation stops. Limber's equation is accurate for
small galaxy separations but breaks down beyond a certain separation that
depends mainly on the ratio sigma/R and to some degree on the power-law index,
gamma, of spatial clustering xi; sigma is the one-sigma width of the galaxy
distribution in comoving distance, and R the mean comoving distance. As
rule-of-thumb, a 10% relative error is reached at 260 sigma/R arcmin for
gamma~1.6, if the spatial clustering is a power-law. More realistic xi are
discussed in the paper. Limber's equation becomes increasingly inaccurate for
larger angular separations. Ignoring this effect and blindly applying Limber's
equation can possibly bias results for the inferred spatial correlation. It is
suggested to use in cases of doubt, or maybe even in general, the exact
equation that can easily be integrated numerically in the form given in the
paper.
