A spot of maths on the train…

But first…
Dulltown, Europe: Today’s random dictionary words are: pennill, pennon, peneplain, pensil, pennyroyal, and rodomontade.
Please have these words looked up and placed in suitable sentences ready for Professor Mouldie first thing after breakfast tomorrow morning. Should the professor decide to conduct the whole lesson in Russian you must pretend to understand and do your best to keep up.

The last time I went on the train to the city of York (about fifty miles north-west of Dulltown) I noticed that beside the tracks between Sherburn-in-Elmet and York there are some old rusty distance marker posts set in the ground every quarter of a mile. They seem to be made of cast iron and are about two feet high. At every whole mile they give the distance to the next station, and in between these there are specially shaped quarter-mile markers at the appropriate points.
They are rather cleverly designed so that even if they are covered in snow or seen in bad visibility the train driver can read the distance by their shape, even if the figures on them are obscured. The one-quarter mile post has a disc with a pointy hat on, the half-mile one (or two-quarters) is a disc with two pointy ears, one each side, and the three-quarter mile one has a pointy hat and two pointy ears sticking out. The driver can see at a glance whether it is a one, a two, or a three-quarters of a mile marker. A nice simple, but efficient design. (I looked online for pictures of this type of marker for you, but strangely I couldn’t find any.)
As I watch the green Yorkshire countryside slip past the window I remembered reading a Sherlock Holmes story, (was it Silver Blaze?) where Holmes surprised Watson by accurately estimating the speed of the train they were travelling on. Watson, as I recall, had noticed that there were no quarter-mile posts visible, and wondered how Holmes had worked out the speed. Holmes explained that he happened to know how far apart the telegraph poles were placed beside the track, which made the calculation quite straightforward… Did Holmes time the intervals between poles using his heartbeat, or did he use his rather nice old pocket watch?… I can’t recall…
To pass the time, and as the markers were obligingly zipping past the window making it a bit easier for me, I thought that I might have a go too…
Right then… Speed is distance divided by time – miles per hour – Yes Dave, that’s what we want… Right then… the distance between markers is a quarter of a mile, now let’s time that… Yes, according to my watch, it takes bang on 9 seconds between markers. Good! Now then, the maths… Er… It’s been a while since I… er…
So, we have the time in seconds: a minute, is 60 seconds, and an hour, is 60 minutes, so an hour must be 60 x 60 seconds. That’s 3,600 seconds… Are you with me so far?… I think I’d better jot this down… Right then, a quarter-mile is covered in 9 seconds, so a whole mile will be covered in four times 9 seconds, that’s 36 seconds. So, how many miles will be covered in one hour? Yes Dave, that’s what we want to know… Well it’s an hour’s worth of seconds, 3,600, divided by our 36… Oh, that’s a 100! We are going 100 miles per hour! That’s a hell of a lot faster that Holmes and Watson would have gone. Phew!…
Ah, now we are slowing down, I expect that’ll be York coming up… Oh, I do feel refreshed!…

About Dave Whatt

Grumpy old surrealist artist, musician, postcard maker, bluesman, theatre set designer, and debonair man-about-town. My favourite tools are the plectrum and the pencil...
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4 Responses to A spot of maths on the train…

  1. I was forced to watch a 1960s railway documentary at the weekend. In it they described a way of calculating the speed of a train. I’m surprised ol’ Sherlock didn’t use it.
    It suggested that you need to count the ‘clicks’ that the wheels make as they go over the joints in the track. The number of clicks in 45 seconds would be the same as the number of miles in an hour.
    Must check it against your pointy head markers one day!

    • Dave Whatt says:

      Well thank you for that Stewart. These days they apparently have welded track without joints – so I don’t think it would work… Still, this is all great fun isn’t it?

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