Each and every railroad corporation, organized or doing business in this state, under the laws or authority thereof, shall have and maintain a public office, or place in this state for the transaction of its business, where transfers of shares of its stock shall be made by such railroad corporation, upon the request of the owner of shares thereof, presenting the certificate thereof. Every such railroad corporation shall keep a book in which the transfers of shares of its stock shall be registered, and another book containing the names of its stockholders, which book shall be open to the examination of the stockholders.
610 ILCS 15/1