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### Where did Fahrenheit and Celsius Come From?

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Date: 07/26/97 at 16:39:30
From: Kyle
Subject: Relations of numbers

How did scientists figure out the relation between two numbers that
mean the same thing, e.g. 0 deg C and 32 deg F? Is there a formula? If
so what is it?
```

```
Date: 07/29/97 at 11:21:16
From: Doctor Rob
Subject: Re: Relations of numbers

I know the story of this one.

Fahrenheit used for his zero degrees the temperature of saturated salt
water at the freezing point, and for his 100 degrees he picked his own
body temperature. He must have been running a slight fever that day,
since normal body temperature is actually 98.6 degrees, not 100. The
boiling point of water he measured as 212 degrees, and the freezing
point as 32 degrees.

The centigrade or Celsius system has its zero at the freezing point of
distilled water, and 100 degrees is the boiling point of distilled
water, and normal body temperature is 37 degrees Celsius.

To figure out the conversion from one to the other, a first-degree, or
linear, function was believed to be correct. This is based on the
fact that materials expand linearly with increased heat. If a material
expands a certain amount with an increase of a certain amount of heat,
then it expands twice as much with twice the increase. If we denote
the Fahrenheit temperature by F, and the Celsius temperature by C,
then we know that when F = 32, C = 0, and when F = 212, C = 100.
We use the two-point form for the equation of a line, and find that

(F-32)   (212-32)
------ = --------
(C-0)    (100-0)

If we simplify this, we get F = (9/5)*C + 32 when we solve for F, and
when we solve for C we get C = (5/9)*(F - 32).

This line does pass through the two points (F, C) = (32, 0) and
(212, 100), and also (98.6, 37).

There are similar stories for other unit conversions, such as meters
to feet, pounds to kilograms, and so on.

I hope that this is what you wanted.

-Doctor Rob,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School History/Biography
Middle School History/Biography
Middle School Temperature

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