A second teenager from the Mount Vernon area was arrested early yesterday and charged with arson in the fire that caused $4.5 million in damage to Fort Hunt High School last weekend, officials said.

Timothy Greer, 19, who graduated from the school last spring and is the son of an Army major general, was arrested at 5 a.m. by Fairfax County police in connection with the blaze that forced the closing of the school for the rest of the academic year, according to authorities.

On Friday night, Robert Smithwick, 18, a reserve forward on the Fort Hunt basketball team, was arrested and charged with arson in the fire just before he was scheduled to play in a varsity game at Mount Vernon High.

Police are looking for a third Fort Hunt student in connection with the early morning fire that gutted a portion of the school and forced relocation of its 1,745 students.

The fire has angered many students and neighborhood residents and, according to Deputy Commonwealth's Attorney Steven A. Merril, Fort Hunt students provided important leads to investigators.

Although Merril refused to give complete details of the alleged arson, he said police are convinced only three teenagers were involved. "This was an act of vandalism at its worst," Merril said. "You are never going to find a satisfactory reason to explain the extent of the damages."

According to Fort Hunt students and faculty members interviewed yesterday, rumors about who might have set the fire obsessed students on Thursday as they relocated to Groveton High School for temporary half-day sessions.

The prevailing theory among students interviewed is that the burning of the school was planned at a party.

Students who spoke to a reporter said they understood the fire was started by persons who broke a window outside the principal's office, poured in gasoline and ignited it from outside.

While not commenting on that account, Meril said there is no evidence the school was entered before the fire. He said it was started near the principal's office with a flammable liquid, most likely gasoline.

Last Saturday's fire was not the first major act of vandalism at Fort Hunt this year, according to assistant principal Stewart Christiano.

In october, he said, vandals cut down the school's flag pole with a pipe cutter, and then rammed the pole through a window in principal James E. Manning's office. On the last school day before the Christmas break, vandals poured motor oil over the floor of a hallway, causing several students to slip and fall. Christiano said. School officials have been unable to identify the students responsible, he added.

According to one school official, neither Smithwick nor Greer, who were described as close friends, had been linked to any past incident of vandalism.

Greer, who is being held in lieu of $25,000 bail at the Fairfax County jail, is a student at Northern Virginia Community College, according to a family friend.

Maj. Gen. Thomas V. Greer, the youth's father, is the director for management in the office of the Army Chief of Staff at the Pentagon. Reached by phone at home yesterday, Greer had no comment on his son's arrest.

The Greers, according to a neighbor, returned in December 1977 to their home at 8408 Brewster Drive in the Mount Vernon section of the county after several years in Hawaii. Timothy Greer is one of four children.

Smithwick, a senior at Fort Hunt, is the son of Edward F. Smithwick, a widower and retired Army officer. The senior Smithwick, who frequently has served without pay at Fort Hunt as a substitute teacher, runs the baseball program of the Fort Hunt Youth Athletic Association, according to a family friend.

Smithwick also refused yesterday to comment on his son's arrest.

Both Smthwick, who is being held in lieu of $50,000 bail, and Greer will be arraigned Monday in Fairfax County General District Court.