The Dundee and Arbroath Railway opened in 1838. It was absorbed by the larger Caledonian Railway, but when the North British Railway completed the construction of the Tay Bridge in 1878, it was granted part ownership of the line to enable it to form its main line to Aberdeen, so the line became the Dundee and Arbroath Joint Line.

Reference:
https://en.wikipedia.org/wiki/Dundee_and_Arbroath_Railway (accessed 13Nov2020)