# 18.2 Variation

**Direct Variation • Inverse Variation • Joint Variation • Calculating the Constant of Proportionality**

Scientific laws are often stated in terms of ratios and proportions. For example, Charles’ law can be stated as “for a perfect gas under constant pressure, the ratio of any two volumes this gas may occupy equals the ratio of the absolute temperatures.” Symbolically, this could be stated as ${V}_{1}\hspace{0.17em}/\hspace{0.17em}{V}_{2}\hspace{0.17em}=\hspace{0.17em}{T}_{1}\hspace{0.17em}/\hspace{0.17em}{T}_{2}\hspace{0.17em}.\hspace{0.17em}$ Thus, if the ratio of the volumes and one of the values of the temperature are known, we can easily find the other temperature.

By multiplying both sides of the proportion of Charles’ law by ${V}_{2}\hspace{0.17em}/\hspace{0.17em}{T}_{1}\hspace{0.17em},\hspace{0.17em}$ we can change the form of the proportion to ${V}_{1}\hspace{0.17em}/\hspace{0.17em}{T}_{1}\hspace{0.17em}=\hspace{0.17em}\; ...$

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