Linear Interval Scale/Examples/Fahrenheit and Celsius

Examples of Linear Interval Scales

Let $\Theta$ be a temperature measured as $F$ on the Fahrenheit scale and $C$ on the Celsius scale.

Then $F$ and $C$ obey the relationship:

$F = \dfrac 9 5 C + 32$

Hence corresponding temperatures can, for example, be tabulated thus:

$\quad \begin {array} {c|rrrr} \cels & 0 & 10 & 20 & 40 \\ \hline \fahr & 32 & 50 & 68 & 104 \end {array}$

and linear interpolation can be used to determine values between those tabulated.

Thus we see that the ratios of the differences are $\dfrac 9 5$ throughout, for example:

$\ds \dfrac {104 - 68} {40 - 20}$

$=$

$\ds \dfrac 9 5$

$\ds \dfrac {50 - 32} {10 - 0}$

$=$

$\ds \dfrac 9 5$

and so on.