Here are the magnificent 19th Century arches of Liverpool Street Station, seen from Exchange Square.
Liverpool Street Station opened in 18751
Now the question is: what curve is that arch? I thought it might be a CYCLOID. A cycloid is the shape made by a dot on the edge of a rolling wheel. I made an experiment.
If you can’t see the video, here is a series of stills:
I imagine that the person2 who designed Liverpool St Station considered that a cycloid was an appropriate form for an arch that was going over rolling stock.
Exchange Square is to the North of Liverpool Street Station. It was opened as part of the Broadgate development in 1991, and covers the railway lines which lead out of Liverpool Street. Before this, the railway lines were uncovered.
Liverpool St Station pre-1962. See the arch in the background. This is now above a tunnel, as the trains go under Exchange Square. Picture credit: Spitalfields Life website. 
1966 
Today
“The main line express platforms of Liverpool St station, 07/66. Scanned photograph taken with a Kowa SET camera”
Today: The platforms north of the station are covered by Exchange Square
My sketching at Exchange Square was interrupted by torrential rain. Twice. I finshed the drawing at home.
Rain. 
Admire the edging. 
After the rain.
1Dates are from “The history of Liverpool Street Station” on the Network Rail website: (downloaded 23rd May 2020)
2 The buildings of Liverpool St Station were designed by Edward Wilson, Chief Engineer of the Great Eastern Railway, according to Victorian Web (http://www.victorianweb.org/technology/railways/69.html) and other sources. Some of his office buildings which surround the station are listed, and his name is in the listing. I can’t ascertain whether this was the same person who designed the arches at the other end of the station. Here’s the listing page from the Historic England site.
Jane Sketching 