A comprehensive railway network was established throughout the UK well before the 1870s although until the big amalgamation in 1923 into four big companies there was a multiplicity of smaller companies. However they often held running rights over each other's territory. It is possible that your ancestors travelled to Plymouth by sea - there could have been some link issued with their tickets but in my opinion it would have been much more likely they travelled by train - Glasgow or Edinburgh to London, London to Plymouth by one of the southern rail companies. They might have had to overnight in London - it would depend on train connections and they would have had to travel from King's Cross or Euston to Waterloo for the connection but I doubt if it would have been longer than the two days in any case. You could look up train journeys but I think it will come out at about 6 hours from Scotland to London and about four hours to Plymouth - but don't quote me on that. Hope this helps.