The district attorney of each county contained within the city of New York is hereby vested with the power to appoint and at pleasure to remove any assistant district attorney attached to his office. The number of such assistant district attorneys and deputy assistant district attorneys for which there is now provision by appropriation and the salary paid to each of them shall be continued except as hereinafter provided. All deputy assistant district attorneys shall become and hereafter be known as assistant district attorneys. The number of assistant district attorneys and the salary paid to any assistant district attorney may be increased or decreased by the mayor of the city of New York with the consent of the district attorney.