Armstrong & Co., Inc., was a registered broker-dealer. Armstrong conducted 1 percent or less of its transactions through members of the national securities exchanges but regularly engaged in and valued that part of its business. Robert Schwartz (defendant) served as Armstrong’s underwriter’s counsel. Armstrong underwrote the issuance of 150,000 Triangle Instrument Co., Inc. (Triangle) shares. The underwriter’s agreement required that all shares be sold within 45 days; funds be returned to purchasers if all shares were not timely sold; and, if all shares were timely sold, Armstrong pay Triangle $230,000 and receive a commission and accounting and legal fees. Triangle pressed for a closing after 45 days, but the entire issue had not been sold. Although Schwartz knew that Armstrong’s individual customers had purchased and paid for 30,000 shares, Schwartz arranged for Sterling Factors (Sterling) to lend Armstrong $115,000 secured by a pledge of all 150,000 shares. Schwartz was indicted and convicted for conspiring to violate § 8(c) of the Securities Exchange Act of 1934 (Exchange Act) and Rule 8c-1, which prohibited a broker or dealer who transacted a business through a national exchange from pledging securities carried for customers’ accounts if the hypothecation subjected the securities to a lien greater than the customers’ indebtedness on the securities. The court found that the hypothecation of all Triangle shares exposed Armstrong’s customers to the risk of not receiving the shares for which they had paid. On appeal, Schwartz argued that (1) the phrase “transacts a business” was so indefinite that it made § 8(c) void for vagueness, and the statute was not applicable to him because only 1 percent or less of Armstrong’s business was conducted through national-securities-exchange members; and (2) the hypothecated securities were not carried for the accounts of Armstrong’s customers when they were pledged to Sterling.