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arbitrary constants arbitrary function axis of Py Baker University bidirectrix congruences Brussels Paper canonical form cidences coefficients coincidence congruences congruence possessing coin congruence whose canonical congruences characterized congruences which possess conjugate nets conjugate system const correspond by duality corresponding asymptotic curve covariant differential equations directrix of Py dual congruence E. J. Wilczynski exist congruences focal sheets focal surface geometry of curved gives kind of Py Let the coordinates linear complex lines indeterminate non-degenerate congruence possesses osculating parametric curves point Py point with respect possess the coincidences Projective differential geometry properties and canonical Py and Pt Py coincides Py referred ray of Py riXi second kind semicovariants seventh integrability conditions sub-group substituted surfaces Second Memoir surfaces Sy Sy aref Sy at Py tangent plane tetrahedron theory of congruences tions Transactions transformation twelve coincidences twelve possible coincidences W-congruence whence