We are relying on Maine for from twelve to fifteen thousand on the 12th of September, and Indiana will answer with from fifteen to twenty thousand, and hearing these two votes the Nation in November will declare for Hayes and Wheeler.* * This being a newspaper report, and never revised by the author, is of necessity incomplete, but the publisher feels that it should not be lost COOPER UNION SPEECH, NEW YORK. *Col. Robert G. Ingersoll of Illinois last night, at Cooper Union, spoke on the political issues of the day, at unusual length, to the largest and most enthusiastic audience which, during the last ten years, any single speaker has attracted. His address was in his happiest epigrammatic style, and was interrupted every few moments either by the most uproarious laughter or enthusiastic cheering. It is no exaggeration to say that the meeting was the largest Cooper Institute has seen since the war. Not merely the main hall was filled, but the wide corridor in Third Avenue, the entrance hall in Eighth Street, and every Committee-room to which his voice could reach, though the speaker was unseen, were crowded--in fact, literally packed. Half an hour before the hour named for the organization of the meeting, admission to the body of the hall was almost impossible; and selected officers, and the speaker of the evening himself had to beg their way to the platform. The latter was as painfully crowded with invited guests as the body of the hall; and ingress was impossible after the speaker began, and egress was almost as difficult owing to the pressure in the committee-room through which the platform is approached. Not only in numbers alone, but in the prominence of the persons present, was the meeting impressive. Besides the usual large quota of active politicians always seen at such meetings, there were seen numbers of leading merchants, financiers, and lawyers of New York, prominent officials not only of the City but the State and National Government. The speech was nearly two hours In length, but as the interruptions were frequent, indeed almost continuous, it seemed very short, and when Mr. Ingersoll concluded his fire of epigrams, there were loud calls and appeals to him to go on. There were suggestions by some of the managers, of other speakers who might follow him, but the presiding officer wisely decided to submit no other speaker to the too severe test of speaking on the same occasion with Mr. Ingersoll.