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Line 14 - A bridge under construction on Duke Street in Alexandria was nearly fully constructed by late September 1797, but its completion was dependent on private subscriptions. On 4 Oct. 1797, Alexandria merchant William Hartshorne sent GW "the Subscription paper" for his consideration, and asked him to make a contribution. Two days later, GW informed Hartshorne that he was enclosing "a check upon the Bank of Alexandria for twenty five dollars". GW added that he was barred from contributing more money because his "expences" ran "high," while his "finances" were "low". See William Hartshorne to GW, 4 Oct. 1797 [Rotunda | Founders Online | Print (Retirement Series, Volume 1, pages 382-83)].
The bridge in question was likely the one across White Oak Swamp, which was known as Harrison's Gut where it emptied into Hunting Creek southwest of Alexandria.
Lines 18-20 - In his diary entry for 12 Oct. 1797, GW recorded that he accompanied both the marquis de Lafayette's son, George Washington Motier Lafayette, and the young man's tutor, Felix Frestel (Frestal), to Georgetown, where the two Frenchmen planned to "take the stage for New York to embark for France." Young Lafayette, who had fled France for the United States in 1795, wanted to return to Paris after receiving reports that his father, who had been confined in an Austrian prison, had finally been released. Young Lafayette and his tutor had been staying at Mount Vernon since GW's retirement from the presidency, which explains one reason why GW accompanied them to "the Fedl. City." GW noted in his diary that he returned home on 13 October. See Diaries, 6:236-37, 261-62.