644 CHEMISTRY: BURDICK AND ELLIS 
r = 1 
n n+l 
. . . + (-1)"+' t/(0) = 0 
identically. If U (/) "s also homogeneous, the functional defined by the 
equation 
n 
w (fuh, ...,/„) = c/ (/,+ ...+/„)- 2 Vi+ ••• + 
...+/„)+... +(-l)»C/(0) 
is easily proved to be linear in each of its arguments. Iifi=f2= . . . =/, 
it follows from definition and the condition of homogeneity, that 
W(f,f, . . .,f)^K„U(f), 
where 
A'„ = 2 (- 1)- ^ (n-1) . . . (n-r+l) _ 
But this expression can be proved equal to n! which cannot vanish for 
any positive value of n, and since the w-linear functional W can be ex- 
pressed as a multiple Stieltjes integral the homogeneous functional 
U (/) of order n can be put in the same form. 
1 Riesz, Ann. Sci. Ec. norm., Paris, (Ser. 3), 28, 1911, (36^3). 
^Ibid., 31, 1914, (9-14). 
3 Fr^chet, New York, Trans. Amer. Math. Soc, 16, 1915, (215-234). 
THE CRYSTAL STRUCTURE OF CHALCOPYRITE 
DETERMINED BY X RAYS 
By Charles L. Burdick and James H. Ellis 
CHEMICAL LABORATORIES. THROOP COLLEGE OF TECHNOLOGY 
Communicated by A. A. Noyes. September 29, 1917j ' 
Introduction. — This investigation of the atomic structure of crystals 
of chalcopyrite (CuFeS2) was undertaken, as no study of a complex 
sulfide by the method of X-rays had previously been carried out. 
Moreover, comparatively few crystals of the tetragonal system, in 
which chalcopyrite crystallizes, have been examined; the only ones 
being certain oxides of the formula MO2 studied by Vega;rd^ and by 
Williams.2 Yet the determination of the structure of crystals belong- 
