# Gas Chromatography Detectors - Detector Linearity > Determination of Response Index > The Logarithmic Dilution Method of Linearity Measurement > Page 10

Now when t=0, C_{t }=C_{o},
where C_{o }is the initial concentration of solute.

Thus, k = log C_{o} and _{}

or _{}

Consequently, if the logarithm of the detector output is plotted against time, then, for a truly linear detector, a straight line will be produced having a slope (Q/V). If the detector has a response index of (r) and the slope of the line is (j), then

_{}

The accuracy of the measurement will depend on the flow rate remaining constant throughout the calibration, and, consequently, a precision flow controller must be employed. Manufacturers do not usually provide the response indices for their detectors and so it is left to the analysts to measure it for themselves. Thus,

"the* linear dynamic range of a detector is that range of concentration of a
solute over which the response index lies between 0.98 and 1.02."*