Re: what is the history behind Newton's law of cooling?

Bonjour Anna,

You're (sort of) in luck ... Newton presented the Law of Cooling in a paper entitled "Scala Graduum Caloris", published (in Latin of course!) in the Philosophical Transactions of the Royal Society of London, in 1701. I found an English translation of this paper online at http://web.bham.ac.uk/winterhs/Newton.htm (Isn't the Web amazing!)

However, reading three-hundred-year-old scientific papers is even harder than reading modern ones. I'll try to sum it up for you, which should make it easier to follow.

Basically, Newton had to make up his own temperature scale - you couldn't just buy a Celcius thermometer back in 1701 - so the first part of the paper discusses how he did this. He thought up a bunch of "reference temperatures" - the temperature at which water boils, the temperature at which metals glow faintly, the temperature at which bismuth melts, etc. He measured the temperatures of these events by asking "How much does 10,000 units of volume of linseed oil expand at this temperature"?

Imagine building a crude thermometer, filled with linseed oil instead of mercury. You raise the temperature of the thermometer, the oil expands and rises up the tube. Then, instead of writing numbers 0-100 on the tube and calling them "degrees Celcius", Newton put little marks on the thermometer and labeled them "lead melts here; water boils here; bismuth melts here" and so on. Newton then put his own numerical scale on the tube, running from 0 (ice) to 192 (red-hot coals), and called the units "degrees of heat".

Then, for the cooling law itself, he heated a "pretty thick piece of iron red-hot". It was put in a cool place, and samples of the "temperature flags" were placed on it - a bit of bismuth, a bit of lead, a drop of water, etc. Newton observed how long it took before the bar cooled enough to solidify the lead, solidify the bismuth, to stop glowing, etc., and comparing these times to the marks on his imaginary linseed thermometer, he deduced that the rate of heat loss was linear with temperature; i.e. "The excess of degrees of heat [temperatures] of the iron ... were in geometrical progression, when the times were in arithmetical progression."

I don't know whether he'd invented enough calculus yet to turn the idea of "geometrical progression" into a differential equation, but that's how the experiment was done.

Interesting stuff indeed! And it gives you an idea of some of the difficulties of doing science way back then ... you had to invent your own temperature scales, know all sorts of chemistry, do all of the math by hand, etc. Newton was an alchemist, remember, so these sort of games with bismuth and tin and red-hot iron was right up his alley.

Hope this helps! Thanks for asking!

-Ben Monreal