A while back I quoted Mark Twain on the subject of Berlin's cab-fare calculator at the end of the 19th century. This was a map where "every street is sectioned off like a string of long beads of different colors". I mistakenly described it as a tramlines map, since Berlin had horse-drawn trams at that time. However it is quite clear from Twain's text that this map was used to regulate hansom-cab traffic.
I have now located an online reproduction of the map dated September 1884. It is described as a Droschken-Wegemesser, a distance calculator for cabs, and it is plain that this is what Mark Twain was describing in his April 3, 1892 article.
The text indicates that each coloured segment was about 160 metres long and about 15 segments, or 2.4 kilometres, could be covered by a cab in a quarter of an hour.
The cabs must have been pretty speedy. Presumably major intersections had traffic policemen, but much of the traffic would have proceeded by the rule of shout and shove.
To ride a bicycle, morning and evening, between the main train station (then the Lehrter Bahnhof) and what used to be the site of the Jerusalem Church takes me 15 or 16 minutes in each direction. My route comprises 21 coloured segments of the map. So on the pedals, I am only about 40 per cent faster than a 19th century A-grade horse.
The reproduction is on a page presenting twelve historic Berlin maps. They have been re-published by the Berlin Public Library and I recommend you visit to see a greatly magnified version (under the heading Mai). Clearly this map is diagrammatic in use, but not diagrammatic in its overall form. The underlying form is a conventional street map.
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