The procedure to determine the wavelength of different spectral lines of mercury light using a plane transmission grating is as follows:

1. Obtain a mercury light source and a plane transmission grating.
   
2. Place the mercury light source on one side of the grating, and set up a screen on the other side to observe the diffracted light.
   
3. Observe the diffracted light on the screen and identify the spectral lines of mercury light.
   
4. Measure the angle between the incident light and the diffracted light for a particular spectral line.
   
5. Use the formula for grating equation to calculate the wavelength of the spectral line:
   
   sin(Θ) = nλ / d
   
   where,
   Θ is the angle between the incident light and the diffracted light,
   n is the order of diffraction,
   λ is the wavelength of the spectral line, and
   d is the grating constant (the distance between two consecutive lines on the grating).
   
6. Repeat the process for different spectral lines to determine the wavelengths of multiple lines.
   
7. Compare the calculated wavelengths with the known wavelengths of mercury spectral lines to confirm the accuracy of the measurement.
   
   Note: This procedure assumes that the grating is a plane transmission grating and that the incident light is collimated.