PHYSICS: C. BARUS 
349 
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, es- 
pecially projectively. Consequently the following theorem 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 Y' 
and at the same time adjoint union curves of the reciprocal congruence T. 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 geodesies but also 
with apparently unrelated concepts; there appears throughout a unifying 
feature, however, in the notion of reciprocal congruences. 
1 Green, G. M., these Proceedings, 3, 1917, (587-592). 
2 Wilczynski, E. J., Trans. Amer. Math. Soc, New York, 9, 1908, (79-120). Cf. top of 
p. 83. 
s Sperry, P., Amer. J. Math., Baltimore, 40, 1918, (213-224). 
4 Green, G. M., loc. cit., pp. 590-591. The congruence referred to is that generated by the 
lines y£. 
5 Green, G. M., Amer. J. Math., Baltimore, 38, 1916, (287-324). 
6 Segre, C., Ac. dei Lincei, Rend., Rome, (Ser. 5), 17 2 , 1908, (409-411). 
7 Darboux, G., Bull. Sci. Math., Paris, (Ser. 2), 4, 1880, p. 356. 
THE RECTANGULAR INTERFEROMETER WITH ACHROMATIC 
DISPLACEMENT FRINGES IN CONNECTION WITH THE 
HORIZONTAL PENDULUM 
By Carl Barus 
Department of Physics, Brown University 
Communicated, September 16, 1918 
1. Introduction. — In the Reports of the Carnegie Institute of Washington, 
1915, No. 229, Chap. I, part 2, pp. 30 et seq., I adduced a method for the 
application of the displacement interferometer to the horizontal pendulum 
with a graphic exhibit of the results obtained during a series of months. The 
concave mirror design by which the spectrum interference ellipses were made 
available showed a very satisfactory performance. The attainable accuracy 
was such that for moderate constants in the installation of the pendulum, an 
inclination of 3 X 10~ 4 seconds of arc should have been registered per vanish- 
ing interference fringe (ellipse), or about 10~ 3 seconds per 10~ 4 cm. of displace- 
