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sible, to supply equivalent treatments, in such cases, which are independent of this notion; not necessarily to replace the older theorems, but to afford new theorems which are frequently of more value in practice. Moreover, it is generally difficult to define order of contact in a purely geometric way, especially projectively. Consequently the following thqorem is not without interest: on any non-ruled surface S there exist three one-parameter families of curves, the members of each family of which are union curves of a congruence r' and at the same time adjoint union curves of the reciprocal congruence r. These are the curves of Segre,6 and the curves of Darboux may be characterized as composing the three families conjugate to them. The generalization of surfaces of Voss described above is only one of the many, instances in which an important metric property of a configuration is really a particular case of a far more general projective one. I have found a number of others, connected not only with the subject of geodesics but also with apparently unrelated concepts; there appears throughout a unifying feature, however, in the notion of reciprocal congruences.

The Rectangular Interferometer with Achromatic Displacement Fringes in Connection with the Horizontal Pendulum