NEW YORK — Exxon Mobil Corp. (XOM) (XOM) on Thursday said its profit rose to $10.49 billion in the third quarter, making it the second-largest quarterly profit ever recorded by a publicly traded U.S. company. The world’s biggest oil company said its net income amounted to $1.77 per share for the July-September period, up from $9.92 billion, or $1.58 per share, a year ago. The results surpassed the expectations of Wall Street analysts. On average, analysts expected the company to earn $1.59 per share in the quarter. Revenue fell to $99.59 billion from $100.72 billion from a year ago, which saw then-record oil prices because of hurricanes Katrina and Rita. The largest quarterly profit ever was Exxon’s $10.71 billion profit in the fourth quarter of 2005.