Assisting the board of trustees there shall be a medical board to be composed of three licensed physicians, one of whom shall be the physician for the county, another of whom shall be appointed by the board of trustees, and the third of whom shall be named by agreement of the other two physicians. If for any reason any regular member of the medical board shall be unable to, or in the judgment of the board of trustees may not properly, act in any particular case, the board may designate a substitute to act on the particular case on the medical board. The medical board shall arrange for and pass upon all medical examinations required and shall perform all other services as may be required of it by the board of trustees, pursuant to this part, and shall report in writing to the board of trustees its conclusions and recommendations upon all matters referred to it. The medical board shall act by a majority of its members.