Specifically from Lauscha in 1862, does anyone know how extensive railways were then?
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2Are you looking for an exact timing or just a rough range? – Steve Bird Jun 27 '17 at 20:37
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Pretty close to this question:the-speed-of-sea-travel-in-the-beginning-of-19th-century – justCal Jun 27 '17 at 20:54
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1The railway line from Probstzella wasn't extended to Lauscha, and Sonneberg until the early 20th century when Lichte station became an express railway station. – sempaiscuba Jun 27 '17 at 22:09
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More generally, you can read more about the History of German railways on Wikipedia, which would give you the basic information you'd need to work out an estimate. – sempaiscuba Jun 27 '17 at 22:13
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(The maps are from an Atlas Obscura article on Isochronic maps and the wikipedia entry on German Railways.)
Here's an isochronic map centered on London from the early 1880s to give a feel of how long it would take ~20 years later:
The German rail network in 1861 suggests there already was a track nearby (you can see a track between Eisenach and Bamberg if you zoom in) so the travel time would likely have been within 10 days in 1862 as well:
For completeness, the travel times in 1914 to illustrate how fast things evolved back then:
Denis de Bernardy
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2I sure hope this answers the question, because I'm upvoting for the maps regardless. – T.E.D. Jun 28 '17 at 21:12