larger number of facts as being the more useful, and, in his estimation, this meant that the phase rule was of much greater significance than the collection of hypotheses that went under the name of solution theory. Whereas the theory of solution was rife with exceptions and adequately described only those solutions approaching infinite dilution—"slightly polluted water" was Bancroft's pungent phrase—the phase rule was perfectly general. "The beauty of the phase rule is that, though qualitative, it is absolute and applies to every case of equilibrium. . . . It is therefore the framework on which everything must rest."22

Bancroft's enthusiasm for the phase rule dimmed only slightly in later years; his skepticism about the study of dilute solutions, and chemists who studied them, altered not at all. Ironically, when G. N. Lewis and A. A. Noyes developed the concept of activity to extend the range of applicability of the equations of chemical thermodynamics from ideal to real solutions, Bancroft could only see mathematical juggling—a desperate attempt to make experimental data conform to theoretical predictions. Lewis and Mary Baker Eddy, he wrote, were "the Gold Dust Twins of Christian and Physical Science. Mrs. Eddy eliminates sickness but admits error. Lewis admits sickness but eliminates error."23 Friendly colleagues viewed Bancroft's passion for the phase rule as an eccentric but harmless enthusiasm; some members of the "dilute school" understandably saw it as reckless and irrational. A. A. Noyes, it is said, refused to allow the library of Caltech's Gates Chemical Laboratory to subscribe to Bancroft's journal.24

Although Bancroft's identification with the phase rule was so strong as to lead some of his students to nickname him "The Phase Ruler," Bancroft's concern with making knowledge useful found other avenues for expression. He and his students conducted numerous studies of such im-

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