576 
PHYSICS: C. BARUS 
at a. If iV2^ be projected from a it becomes a Kummer surface. 
There is a family of oo^ surfaces M2^^ with the same G2.81. By pro- 
jection we obtain a family of N2^'s whose node a runs over a quartic 
spread — the simplest invariant of G25920. The 10 points in the ^4 
of / run over the Hessian Jio of Ji. The spread is its own Steinerian 
and the polar cubic of a point a on Ja as to J4 is a Segre cubic spread 
with nodes at the 10 points on Jio, and of course a simple point at a. 
The point a on its polar cubic determines a binary sextic — the funda- 
mental sextic of the hyperelliptic functions. In this way the solution 
of the form problem of G25920 in terms of hyperelliptic modular functions 
becomes apparent at once in the special case when J4 = 0. This re- 
striction is removed later by a conventional method. The conclu- 
sions above all are drawn from the existence of a set of 9 quadrics whose 
complete intersection is the normal spread If 2^^ and whose coefficients 
are the modular forms a. 
The above determination of the lines of O differs from that of Klein^ 
in that no equation of degree 27 or other resolvent equation is em- 
ployed. All the processes are effected within the domain of the in- 
variants and linear covariants of Klein also uses as fundamental 
form problem that of the Maschke collineation group in ^3 rather than 
the Burkhardt form problem. This implies the isolation of a root of 
the underlying binary sextic. The accessory irrationalities required 
are thereby somewhat simpler. 
1 These Proceedings, 1, 245 (1915); Trans. Amer. Math. Soc, 16, 155 (1915). This 
series of investigations has been pursued under the auspices of the Carnegie Institution of 
Washington, D. C. 
2 These Proceedings, 2, 244 (1916); Trans. Amer. Math. Soc, 17, 345 (1916). 
3 That an equation of degree 27 for the lines of a cubic surface could be solved by hy- 
perelliptic modular functions was first pointed out by Klein, /. Math., Paris, Ser. 4, 4, 169 
(1888). His suggestions were elaborated by Witting, Math. Ann., Leipzig, 29, 167 (1887); 
by Maschke, Ibid., 33, 317 (1889); and by Burkhardt, Ibid., 35, 198 (1890), 38, 161 (1891), 
41, 313 (1893). 
THE INTERFERENCES OF SPECTRA BOTH REVERSED AND 
INVERTED 
By Carl Barus 
DEPARTMENT OF PHYSICS, BROWN UNIVERSITY 
Received by the Academy, September 6, 1916 
This is an interesting combination of the two methods of investiga- 
tion hitherto given (Carnegie Publications, No. 249, 1916, §4) and not 
very difficult to produce. Retaining the adjustment for inverted spectra 
