The orientation density distribution of fibres in a sheet of paper must be characterized in a way to take into account its involvements in the physical properties of the paper. We are used to defining this distribution in number of fibres n, per angular interval in the plane of the sheet. But, it is less frequent to show that this definition involves the density distribution, in the different directions in the plane of the sheet, of the cumulated length of the fibres rectified as line segments. Taking this into account, we can define a length-weighted orientation density distribution n,, = l , n$A, where l, is the average length of the B-oriented line segments and A is the average length of all the fibre segments. The two expressions of n, and n,, are equal when the average directional length of the fibre segments &is constant over B. In general, 1, varies with B, having maximum near the machine direction and being further influenced by the mechanism of drainage. The length-weighted orientation density distribution can be rigorously defined from the radius of curvature R(0)of a curve called the equivalent pore. It represents the figure delimited by the fibres considered as sequenses of connected straight segments at the boundary of the pores of the fibrous network. Moreover, the equivalent pore is homothetic to the average pore that one can build from the measurement of the average directional secants of the pores in the plane of the sheet. This geometrical concept illustrates a physical reality that the definition of the classical 'number-weighted' orientation distribution, n, does not bring apriori into the open. Numberous results and simplifications arise from the concept of the equivalent pore for the study of the physical properties of paper. Now, a narrow light beam incident on a sheet of paper propagates by following the fibres in the plane of the sheet and is subdued in each direction according to the number of intercepts between a fibre and its neighbouring fibres. The optical image obtained reveals the characteristic shape of the equivalent pore and can be used to defined the orientation distribution of the fibres. The anisotropy of the orientation density distribution of the fibres as measured by n,,is characterized by one parameter only (the ellipticity db) , when the equivalent pore is an ellipse. We have verified many times that this shape applies for most machine-made papers. Thus, n,, is expressed using functions of elliptic nature or their development in trigonometrical series, the ellipticity d b being the only parameter used. The expressions of n,, are more precise and more realistic than other frequently used to characterize the orientation density distribution of the fibres in a sheet of paper. The classic numberweighted orientation density distribution of the fibres n, is advantageously replaced by its length-weighted expressions n,, wherever this funktion appears, for studying the structure and properties of paper.