(14) The electromotive-force necessary to maintain an electric arc of length ${\displaystyle l}$ with a current of intensity ${\displaystyle i}$ has been found by Mrs. Ayrton to be

where ${\displaystyle a}$, ${\displaystyle b}$, ${\displaystyle c}$, ${\displaystyle k}$ are constants.

Find an expression for the variation of the electromotive-force ${\displaystyle (a)}$ with regard to the length of the arc; ${\displaystyle (b)}$ with regard to the strength of the current.