Vol.. 7, 1921 
MATHEMATICS: E. HILLE 
303 
really greater for thick than for thin gold. If the free path is of the order 
of 10 ~ 5 cm., that is, comparable with the thickness of the leaf, then the 
average path in the thicker metal will be longer than in the thinner, and a 
greater departure would be expected in the thicker metal, as found. 
[I am much indebted to my assistant, Mr. J. C. Slater, for his skill in 
making the readings.] 
1 Maxwell, C, Everett, J. D. and Schuster, A., B. A. Rep. 1876 (36-63). 
2 Bridgman, P. W., Physic. Rev., Ithaca, (2), 17, 1921 (161-194). 
AN INTEGRAL EQUALITY AND ITS APPLICATIONS 
By Einar Hiu,E 
Harvard University 
Communicated by G. D. Birkhoff, May 15, 1921 
The purpose of this note 1 is to deduce an integral equality adjoined to 
a linear homogeneous differential equation of the second order and 
to show some applications of such equalities to the question of the dis- 
tribution of zeros of solutions of such differential equations in the complex 
plane. 
Let G(z) and K(z) be two single-valued and analytic functions of z 
throughout the region under consideration and take the differential equation 
or the equivalent system 
(2) with 
dz K(zY 
From this system we easily deduce the relation 
Zl -» Zl 
where u denotes the conjugate of u. If we put 
(4) dK = ™, dT = G(z)dz f 
relation (3) becomes 
or, split up into real and imaginary parts, 
