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THE LAST WORD

Hot in the hayI have always assumed that the belief that haystacks can burst into flames spontaneously was a convenient myth to cover for careless farm workers having a crafty cigarette break while forgetting their surroundings, but a friend insists that it can happen. Surely the only way hay can warm up significantly is if it is wet and bacteria begin to heat the stack as part of the process of biodegradation. But I’d be amazed if this could generate temperatures hotter than about 40 ºC. So how else could ignition take place? (Continued)

n Insurance companies in the 18th century insured farmers’ haystacks in England, Scotland and Wales, so they clearly believed fire was possible. A standard phrase in the policies reads: “Free from loss on such hay or corn as shall be destroyed or damaged by its natural heat.” This clause appears hundreds of times in the policies of Sun Fire Office in London.Derek MorrisBy email, no address supplied

Train brain drain If I don’t know the time of the next half-hourly train to depart from my local station, is there any point in running to the station? My wife tells me it won’t make any difference to whether I catch the next train or not, but I insist it will. I must admit, my journey time door-to-door does not seem to be affected by the speed of my approach to the station.

n If you arrive at the railway station at some random time, regardless of how fast you travelled to the station, you will have to wait an average of 15 minutes and a maximum of 30 minutes for the next train.

So running will not make any difference to your average waiting time at the station.

However, if you arrive 1 minute earlier by running than by walking then on one trip in 30 you will catch a train that you would have missed if you had walked, therefore arriving at your destination 30 minutes earlier.

On the other 29 out of 30 times that you don’t catch an earlier train, you will have to wait 1 minute longer on the platform than if you had just walked there. On these occasions the trip will probably seem longer, although the actual door-to-door time remains unchanged.

You save 30 minutes once in 30 trips, so on average the 1 minute saved by running saves 1 minute door-to-door. If you save more than 1 minute by running, you’ve got a better chance of catching the train and saving 30 minutes more often. The average time saved always matches the time saved by running.Brian HortonWest Launceston, Tasmania, Australia

n If your run gets you to the station 3 minutes earlier, then one day in 10 you will get to work half an hour earlier. So your wife is wrong. But perhaps she meant that the average waiting time at the station will be unaffected. This is true: nine days out of 10 you will wait 3 minutes longer, exactly balancing the one day in 10 that you save 27 minutes.

None of this explains the fundamental question underlying this paradox: why not look at the train timetable? If you are uncomfortable with smartphone apps, timetables still exist in old-fashioned paper form.Ian Gent and Judith UnderwoodCupar, Fife, UK

Not so plain thinkingThe editor writes… An aircraft must keep up a certain airspeed to stop it stalling. But when flying into a headwind, it can reduce its ground speed without fear of falling. These facts were stressed by Clive Teale in a correction to our question Plane Thinking on 23 March. The correspondent he was correcting, Len Winokur, had actually made the same point, but his answer was sent off course by the word-traffic controller at the Last Word. Apologies to Len for the error.

This week’s questionsHard quesTioNRecently our lovely soft water, which came from a loch high in

the Cairngorm mountains, has been replaced by slightly hard water which comes from an underground borehole. Our kettle and our hot water tanks now pop and crackle loudly when the water is heating, rather than offering just a gentle hiss as before. Can anybody explain the reason for this odd effect when we are heating water with a higher mineral content?John PoynerNethybridge, Highlands, UK

iNside ouTMammals are supposed to have testes outside the abdomen because their fertility would be impaired if they were kept inside at body temperature. But birds have internal testes, despite having a higher body temperature. Why and how did birds evolve in this way when mammals did not? And why doesn’t this affect the birds’ fertility?Malcolm HalfordMelton Mowbray, Leicestershire, UK

Colour THaT sTiNgsI recently made nettle wine using an old recipe. Nettles (genus Urtica) are green, yet when they were boiled, as the recipe suggested, the resulting liquid was red. Why? Was this a property of the plants or of the aluminium pan, or some residue in the apparently clean pan? Nothing else, such as wine-making yeast, had been added at that stage.Frances CottinghamIsle of Wight, UK

“if you don’t know the time of the next train, running to the station won’t change your average waiting time”

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