Help translating column headers from mantal

[George Lind]

Attached is an image taken from the mantal for Brandstad 1798.
I am interested in the second and third column headers

I believe the second column is the following:
gamla hemmantalet efter jordeboken = old home census after the Land Register

I believe the third column is the following:
nyå hemmantalet efter förmedling = new home number after mediation
 
Is my Swedish correct?   The translations are from Google Translate.  They don't really make much sense.
Can anyone translate these better?

Here are the links to the page

Häradsskrivaren i Frosta och Färs fögderi (M) HIb:45 (1798) Image 4730 (AID: v347067.b4730, NAD: SE/LLA/10907)
https://sok.riksarkivet.se/bildvisning/A0005545_00809


Thanks,
George

[Kalle Birgersson]

Förmedling is an old term for a change of tax level, so one column with the old tax according to the land register (jordebok, earth book) and another one with the new tax.

[George Lind]

Kalle,
Thanks for all your help.
George