Every railroad corporation shall start and run its cars for the transportation of persons and property at such regular times as it shall fix by public notice, and shall furnish sufficient accommodations for all such persons and property as shall, within a reasonable time previous thereto, offer or be offered for transportation at the place of starting and the junction of other railroads and stopping places established for taking and leaving persons and property, and shall transport between such places all such persons and property on the payment of its lawful charges therefor: provided, such corporation may decline to receive any person afflicted with any contagious disease, or otherwise unfit to be admitted into its cars.