sums of money which are being spent by companies in bringing
small unit plants to develop the processes which have been
worked out in the laboratory, demonstrate that practical
results are being secured.

Where there have been sympathy and hearty cooperation between
the Mellon Institute and the company concerned, the institute
has been able to push through to a successful conclusion large
scale experiments in the factory of the company, which in the
beginning of the fellowship seemed almost impossible: it may be
said that the results of the fellowships at the Mellon
Institute indicate that a form of service to industry has been
established, the possibilities of which no man can say.



A FEW CLASSIC UNKNOWNS IN MATHEMATICS

BY PROFESSOR G. A. MILLER

UNIVERSITY OF ILLINOIS

KING HIERO is said to have remarked, in view of the marvelous
mechanical devices of Archimedes, that he would henceforth
doubt nothing that had been asserted by Archimedes. This spirit
of unbounded confidence in those who have exhibited unusual
mathematical ability is still extant. Even our large city
papers sometimes speak of a mathematical genius who could solve
every mathematical problem that was proposed to him. The
numerous unexpected and far-reaching results contained in the