Murray Hill, N. J. Bell Telephone Laboratories, Incorporated November 1, 1954. [1-cover sheet], -5 leaves + four figures on one leaf of plates. 10 7/8 x 8 3/8 inches. A reproduced typescript with four holes punched at the spine as issued. Stapled upper left, with light overall wear and minor creasing.
The Bell Laboratories Filing Subject for this paper is "Network Theory." Very Good. Wraps. 
"It is shown that the resistance of a two-terminal resistance network is a concave function of the component resistances." (abstract)
"Recently, in connection with the design of a certain circuit, a variable resistance was desired. The variation of this resistance as the shaft was turned should approximate a certain function which was convex downward. It was also desired to obtain this behavior from a circuit consisting of one or more linearly wound potentiometers on the shaft and fixed resistors. All the circuits which were studied proved to have resistance curves which were concave downward. Our lack of success led to a theorem on networks which shows that this is necessarily always the case." (first paragraph).
This paper appears to discuss material eventually published as "Concavity of Resistance Functions" by Shannon and Hagelbarger. This technical memorandum was not included in Sloane and Wyner's bibliography.
PROVENANCE: The personal files of Claude E. Shannon (unmarked). There were multiple copies of this item in Shannon's files.
NOT IN Sloane and Wyner, "Claude Elwood Shannon Collected Papers"
Sloane and Wyner, "Claude Elwood Shannon Collected Papers," item 98 ("Concavity of Resistance Functions")