The business of a firm is to be conducted for and in behalf of the members of the firm; but the members may agree that some one member or a third party shall conduct the business and fix his powers and duties and may restrict the common law powers of any member, inasmuch as a partnership has the right to conduct its business through any agency it chooses, as fully and completely, as an individual might. Nevertheless the firm may be bound by the unauthorized act of a member, the formation of a partnership and its existence proclaimed to the world, being, 'prima facie, a declaration to the world of a mutual agency within the scope of the business.