When Jesse L. Jackson was sworn in Wednesday as one of Washington's unpaid "shadow" senators, he said, "I accept the burden of service gladly for statehood and democracy."

Then the senator disappeared. Into the shadows, so to speak.

Asked Wednesday how the District of Columbia's new lobbyist for statehood planned to spend the opening day of the 102nd Congress, a spokesman for his office said, "He'll be out of town."

Whereabouts?

"We can't tell you that," said Unnia Pettus of the National Rainbow Coalition.

Yesterday morning, The Post phoned Jackson's office to arrange a photograph of the shadow senator during his first day on the job. An aide said he had departed the night before for the West Coast.

Then Pettus called back to say the real problem was "a scheduling conflict." Jackson, she said, would be "in private meetings" all day.

With whom?

She wouldn't say.

All out of town?

"Well, not exactly. But Monday he'll be back available to the public."

"I'm not saying where he is. He could be in Northwest Washington or he could be in Europe," she said later.

As it turns out, it was neither. Pettus called back still later with a final clarification. Jackson was in Los Angeles, addressing a convention of independent television executives.

The District's other shadow senator, Florence Pendleton, spent most of the day on Capitol Hill, and the rest at home preparing information packages on statehood for members of Congress.