ALBANY, Jan 26 — Edward F. Cox, a Manhattan lawyer and a son-in-law of President Richard M. Nixon, declared Thursday that he would not run for the Senate this year, even though Republicans had been courting him anew to challenge Hillary Rodham Clinton. The announcement from Mr. Cox ended the prospect of a dynastic clash pitting Mrs. Clinton, a former first lady, against Mr. Cox, who is married to Mr. Nixon's daughter, Tricia. In a statement, Mr. Cox said that "after careful consideration of the circumstances and conditions as they exist surrounding the race, including the now shortened time frame...