On Three Orthogonal Congruences of Curves

In a paper on "Curvilinear Congruences" by Dr. C. E. Weatherburn, published in the Transactions of the American Mathematical Society, Vol. 31 (1929), it has been proved that for three orthogonal congruences of curves, the moments of any two of the congruences in the direction of the third are equal. The object of the present paper is to prove the same result by a different method and also to obtain expressions for the moments and the tendencies in terms of torsions, curvatures, normal angles and the rates of changes of these normal angles.