Washington, Sept. 20. - A rumor has been started that General Russell A. Alger tendered his resignatlon as s,ecreary of war just before he left Washnigton several days ago. Aceording to he story told here, but which lacks official confirmation, General Alger called at the White House and informed the president that he was ready to give up lis office at any time. President McKinley is said to have deelined to accept the resignation. No one in high official circles could be found who would confirm the report, jut it was suggested in several quarters :hat in view of the tour of inspection of southern camps which General Alger s now making it was not likely that he ntended resigning his office at this ;ime.