MAY 20th. —Mr. Walker, the Secretary of War, is some forty seven or eight years of age, tall, thin, and a little bent; not by age, but by study and bad health. He was a successful lawyer, and having never been in governmental employment, is fast working himself down. He has not yet learned how to avoid unnecessary labor; being a man of the finest sensibilities, and exacting with the utmost nicety all due deference to the dignity of his official position. He stands somewhat on ceremony with his brother officials, and accords and exacts the etiquette natural to a sensitive gentleman who has never been broken on the wheel of office. I predict for him a short career. The only hope for his continuance in office is unconditional submission to the President, who, being once Secretary of War of the United States, is familiar with all the wheels of the department. But soon, if I err not, the President will be too much absorbed in the fluctuations of momentous campaigns, to give much of his attention to any one of the departments. Nevertheless Mr. Walker, if he be an apt scholar, may learn much before that day; and Congress may simplify his duties by enacting a uniform mode of filling the offices in the field. The applications now give the greatest trouble; and the disappointed class give rise to many vexations.