Page:Calculus Made Easy.pdf/52

are ${\displaystyle 1570}$ cub. in. and ${\displaystyle 2260.8}$ cub. in. respectively, and ${\displaystyle 2260.8-1570=690.8}$.

Also, if

(5) The reading ${\displaystyle \theta }$ of a Féry’s Radiation pyrometer is related to the Centigrade temperature ${\displaystyle t}$ of the observed body by the relation

where ${\displaystyle {\theta _{1}}}$ is the reading corresponding to a known temperature ${\displaystyle t_{1}}$ of the observed body.

Compare the sensitiveness of the pyrometer at temperatures ${\displaystyle 800^{\circ }}$C., ${\displaystyle 1000^{\circ }}$C., ${\displaystyle 1200^{\circ }}$C., given that it read ${\displaystyle 25}$ when the temperature was ${\displaystyle 1000^{\circ }}$C.

The sensitiveness is the rate of variation of the reading with the temperature, that is ${\displaystyle {\frac {d\theta }{dt}}}$. The formula may be written

and we have

When ${\displaystyle t=800}$, ${\displaystyle 1000}$ and ${\displaystyle 1200}$, we get ${\displaystyle {\frac {d\theta }{dt}}=0.0512}$, ${\displaystyle 0.1}$ and ${\displaystyle 0.1728}$ respectively.

The sensitiveness is approximately doubled from ${\displaystyle 800^{\circ }}$ to ${\displaystyle 1000^{\circ }}$, and becomes three-quarters as great again up to ${\displaystyle 1200^{\circ }}$.