A twisted road, and others may know more than I do, because I haven't tried
to track this. Here's what I remember:

Davenport arrived at Cornell in 1916, just after Knight had finished his
dissertation. So Knight did not take any classes (formally) with Davenport,
nor did Davenport play any role in the supervision of the dissertation
(Alvin S. Johnson and Allyn A. Young were the supervisors). However, the two
men were together at Cornell for the 1916-1917 academic year: Knight was an
economics/statistics (my understanding is that it was primarily statistics)
instructor at Cornell before moving to the University of Chicago in 1917
(for his first stint at Chicago; he left for Iowa in 1919).

Apparently, Davenport urged Knight to submit his dissertation to the Hart,
Schaffner, Marx economic essay competition. The title of the dissertation
was A THEORY OF BUSINESS PROFIT; the title when it was submitted to the
competition was COST, VALUE, AND PROFIT. The essay won second prize, and was
eventually published under the title we all know: RISK, UNCERTAINTY AND
PROFIT.

Knight obviously became familiar with Davenport's work during their year
together; see his essay on Davenport in the Encyclopedia of the Social
Sciences (1931).

Davenport may have played a role in Knight's joining a Veblen reading group
at Chicago in 1917. That group also included Morris Copeland, Clarence Ayers
and Harold Innis. In 1920, Knight published a review of THE PLACE OF SCIENCE
IN MODERN CIVILIZATION in the JPE (vol. 28 (June): 518-20).  

If one wanted to track the influence of Davenport and Veblen on Knight
during these years, the best place to look would be at two unpublished
manuscripts in the Univ. of Chicago Archives:

"The Economic Organization of Society." 25 page annotated outline of an
economics textbook, which Knight probably used as lecture notes at Chicago
when teaching Advanced Economic Theory with J.M. Clark at Chicago in the
summer quarters of 1918-1920.

"Social Organization: A Survey of its Problems and Forms from the Standpoint
of the Present Crisis." A manuscript submitted to the JPE, but never
published. The manuscript has some mention in my essay on "Frank Knight and
The Economic Organization," recently published in my FRANK KNIGHT AND THE
CHICAGO SCHOOL IN AMERICAN ECONOMICS.

Hope that helps, Peter. Anymore you know would help me as well!

Ross Emmett