N.Y. County Law § 386
When the board of supervisors shall have determined to establish a hospital for the care and treatment of persons suffering from tuberculosis, and shall have acquired a site therefor, and shall have awarded contracts for the necessary buildings and improvements thereon, it shall appoint five citizens of the county, of whom at least two shall be practicing physicians, who shall constitute a board of managers of the said hospital. The term of office of each member of said board shall be five years, and the term of one of such managers shall expire annually; the first appointments shall be made for the respective terms of five, four, three, two and one years. Appointments of successors shall be for the full term of five years, except that appointment of persons to fill vacancies occurring by death, resignation or other cause shall be made for the unexpired term. Failure of any manager to attend three consecutive meetings of the board shall cause a vacancy in his office, unless said absence is excused by formal action of the board of managers. The managers shall receive no compensation for their services, but shall be allowed their actual and necessary traveling and other expenses, to be audited and paid, in the same manner as the other expenses of the hospital, by the board of supervisors. Any manager may at any time be removed from office by the board of supervisors of the county, for cause after an opportunity to be heard.
N.Y. CountyLaw § 386