530 
MATHEMATICS: A. B. COBLE 
It is interesting to find that the lithium lines X4602 and X4132 show 
polarized components in the longitudinal effect. The longitudinal 
effects in hydrogen and helium, the only ones investigated up to this 
time, had given unpolarized components. 
Previously, only the diffuse series of elements had shown large electric 
effects which makes the calcium results most unexpected. H and K be- 
long to a principle pair series and the lines of the diffuse series at XX445 7, 
4435, and 4425 show no effect at all, under low dispersion. 
A full account of this investigation will be published shortly in the 
Astrophysical Journal. 
1 J. Stark, Ann. Physik, 43, 965 (1914); J. Stark and G. Wendt, Ihid., 43, 983 (1914) 
J. Stark and H. Kirschbaum, Ihid., 43, 991 and 1017 (1914); J. Stark, Ihid, 48, 193 (1915). 
2 A. Lo Surdo, Roma, Rend. Acc. Unci, 23, 1st. sem., 82, 143, 252, 326 (1914). 
A PROOF OF WHITE'S PORISM 
By A. B. Coble 
DEPARTMENT OF MATHEMATICS, JOHNS HOPKINS UNIVERSITY 
Received by the Academy, August 8, 1916 
The interesting theorem of Professor White^ to the effect that if 
two cubic curves in space admit a configuration Ay — i.e., seven points of the 
one and seven planes of the other such that each of the points is on three of 
the planes and each of the planes is on three of the points — then they admit 
00 1 such configurations furnishes perhaps the only important generali- 
zation of the Poncelet polygons. ^ Analytically expressed the theorem 
states that if for a (3, 3) form i^(X,M) there exists a set of seven param- 
eters X and seven parameters ju such that i*^ = 0 for each X together 
with three m's and for each ju together with three X's, then there exists oo i 
such sets A 7. 
The pubHshed proof of this theorem fails owing to an error of enumer- 
ation.^ This error, originally overlooked by Professor White and my- 
self, was noted subsequently by him. That however the theorem itself 
is true can be shown as follows. 
Let G (Xi, X2) = 0 be the condition that distinct values Xi, X2 determine 
in F (X, m) = 0 the same value of /x. Then G is a symmetrical (6, 6) 
form. If F (X, ju) has a A?, the seven X's constitute an involutorial set 
of G, i.e., a set such that any two of the X's satisfy G = 0. Conversely 
if G has an involutorial set, then F (X, ju) has a A 7. For if Xi and any 
one of X2, . . . 5X7 satisfy G = 0 then, since Xi can determine in F = 0 
at most three /x's, Xi must be associated with three pairs of the remaining 
X's in such a way that each pair determines with Xi a common value y.. 
