Sentence:  With the check came two through tickets—good on the railroad from Hawkeye to Washington via New York—and they were “<WSD>deadhead</WSD>” tickets, too, which had been given to Senator Dilworthy by the railway companies. Senators and representatives were paid thousands of dollars by the government for traveling expenses, but they always traveled “<WSD>deadhead</WSD>” both ways, and then did as any honorable, high-minded men would naturally do—declined to receive the mileage tendered them by the government. The Senator had plenty of railway passes, and could. easily spare two to Laura—one for herself and one for a male escort. 
Meaning of the word marked with <WSD> tags:  Anyone traveling for free.