earth connection ohmic resistance for delicate instruments

Anyone knows what the acceptable earth connection ohmic resistance for delicate laboratory analytical equipments should be? How about the same for the earth well?

I fear the question is rather unclear. Maximum PE resistance is firstly a requirement of safety rules for class 1 equipment (electric safety based on protective earth). State of the art analytical instruments basically shouldn't have additional requirements.

Problems sometimes arise with external connections, e.g. low level analog in- or outputs. They are rather related to lab grounding schemes than ground resistance, e.g. equipment connected to different supply circuits, remote connected devices or data interfaces introducing or affected by ground loops. These problems are mostly instrument specific and can't be addressed by general rules, I think. Some instruments have known weaknesses or design flaws.

Lab practioners and instrument vendor service personal will know various work arounds and special tricks for these devices.

Generally should be less than 4 ohms. But as was stated, this depends by multiple factors.

In the instrument manual under "Earthing requirements" it says "Earth terminal should be properly grounded". What will you do if you see this? What is "Suitably grounded" means?

If the power supply cord constains a protective earth, I would consider plugging it into a correctly wired power outlet as "proper ground".

If the instrument is expected or known to be succeptible to electrical interferences, you should take care that all connected devices (e.g. computer, external sample preparation devices, recorders, whatsoever) are connected to the same power supply circuit. If special wiring instructions are given in the instrument manual, they should be observed.