The Dow Jones industrial average started out weakly today, but as the morning wore on it gathered strength and made steady gains all day. The Dow ended up 25.29 points at 4,787.64. The Nasdaq composite index fell rose 18.72 to 1,045.26. The New York Stock Exchange composite index was up 1.97 to end the day at 313.29. On the Big Board, advancers led decliners 1,467 to 809, with 367.61 million shares traded. The Standard and Poor's 500 stocks rose 4.84 to 585.88. In London, was down $0.05 to close at $383.50.