Daniel Fahrenheit wanted to know how hot things were. So he thought there ought to be a scale of temperature. No-one else had really got going on that sort of puzzle before, so he had to put on his thinking cap.

First of all he thought he ought to find a very cold substance. He made up a mixture of water, ice and a salt called ammonium chloride. The salt we sometimes have on the table is sodium chloride but Herr Fahrenheit used ammonium chloride instead. It's pretty similar stuff, but not quite the same. He mixed a kilogram of water, a kilogram of ice and a kilogram of ammonium chloride together in a large bucket. It turns out that the mixture he made always has the same temperature: it's always as cold as ever it gets. Then he wanted another fixed point on his scale, so he took another bucket and put in it a mixture a water and ice. Then he needed a third, hotter fixed point. Some people think he took the temperature of the inside of a cow, but that is silly nonsense. Herr Fahrenheit was not quite so silly. Actually, he took his own body heat as the upper fixed point. He made a thermometer out of mercury in a glass tube. He put his thermometer in the coldest mixture and made a mark on the thermometer. Then he put the thermometer in the ice water mixture and made another mark where the mercury came to. Then he stuck the thermometer in his mouth and made a third mark where the mercury came up to then. So he had made three marks on his thermometer. He looked at the distance between these three marks. It seemed that the distance between the highest temperature and the middle temperature was about twice as big as the distance between the middle temperature and the coldest temperature.

Now, he wanted to be able to make lots of marks to measure what we call degrees on his thermometer. The easiest way of doing that was to make a scale that easily divided by two. He chose 32 as the number of degrees between the lowest and the middlest temperature, because then he could divide that by two lots of times: 32 Ö 2 = 16, and if you keep cutting that gap in half time after time you get 16, 8, 4, 2, and 1. The distance between the top temperature and the middle temperature had turned out to be twice as big a gap—so on the same scale it would be 64 degrees. So then he heaved a sigh of relief: my thermometer, he said, has three fixed temperature points: ammonium chloride, ice and water we'll call 0 degrees. Ice and water we'll call 32 degrees, and my body we'll call 96 degrees.

Then along came Mr Celsius. He wasn't so interested in the temperature of Mr Fahrenheit's unusual salty mixture. Who ever wants to know the temperature of that? So he used two fixed points: melting ice and boiling water. He called the low point 0 degrees, and the high point 100 degrees.

By now lots of people were using Mr Fahrenheit's scale, but another lot started to use Mr Celsius's scale. So there had to be a way of changing one scale into the other. It turned out that the gap between Mr Fahrenheit's ice water point (32 degrees) and the temperature of boiling water on his scale was about 180 of his degrees. So if he tweaked his scale very very slightly it could be made exactly 180 degrees. If everyone agreed, then it would mean that water boiled at exactly 212 degrees on Mr Fahrenheit's scale. And, what a happy state of affairs that would be, for there are (as you can easily work out) just 180 Fahrenheit degrees between 32 and 212. So 100 degrees Celsius is equal to 180 degrees Fahrenheit! Shazzam!!

Converting one scale into the other turns out to be quite easy. There are two steps. First, remember that ice melts at 32 degrees in the Fahrenheit scale but 0 degrees in the Celsius scale. Then remember that 180 Fahrenheit degrees are as large as 100 Celsius degrees—18 Fahrenheit degrees cover the same range of temperature as 10 Celsius degrees. Now let's convert a temperature of (say) 50 degrees Fahrenheit into Celsius: first, take off 32, giving 18. Then divide by 18. Ha, not too tricky; the answer's just one. Multiply by ten and there you are: the answer's ten degrees. So 50¼F = 10¼C. Here's another one: 68¼F - 32 = 36. 36 Ö 18 = 2. 2 x 10 = 20. So 68¼F = 20¼C. The other way it's even easier: 40¼C Ö 10 = 4. 4 x 18 = 72. 72 + 32 = 104¼F. Wow, that's really hot Mr Fahrenheit!

Once you've got the idea you can make the sums easier. Instead of ten and eighteen we can use five and nine. The proportion is the same: 9Ö5 is the same as 18Ö10. So we say: to convert Fahrenheit temperatures into Celsius, take off 32, multiply by nine and divide by five; and to convert Celsius into Fahrenheit, multiply by five, divide by nine, and then add 32. Now you try!