Line intersect sampling: Ell-shaped transects and multiple intersections

The probability of selecting a population element under line intersect sampling depends on the width of the particle in the direction perpendicular to the transect, as is well known. The consequence of this when using ell-shaped transects rather than straight-line transects are explicated, and modification that preserve design-unbiasedness of Kaiser's (1983) conditional and unconditional estimators are presented. A case against treating multiple intersections as multiple probabilistic events is argued on the basis, also, of preserving design-unbiased estimation.