karlok:
The measurement is from the voltage divider (battery's 9V pole) to A1, and the switch is controlled by a relais, so that there isn't always current flowing.
What is the "ground leg of the voltage divider"? Do you just mean ground?
I was only suggesting an alternative to using a relay to control whether the voltage measurement circuit draws current. R3 and R4, in the schematic, form a voltage divider and test load for the battery. Where R4 connects to ground, I am suggesting connecting instead to an Arduino input/output pin. Under software control, you can make this pin "low" (~= ground) or make it an input, which will not flow any current to speak of. Then R3 can go straight to your battery, and no need for a relay.
The Arduino pins cannot handle much current, so you might have to use larger values for R3 and R4, to get the current under 20mA. Another alternative would be to use a transistor, like a 2N3904 which can handle 200mA in this situation, to control the R4 ground connection.
I'm not sure how important it is that the test load you place on the battery is substantial. The less substantial the load may be, the simpler the circuit can be. The relay approach could place a 1,000mA or larger load. A small transistor could handle up to 500mA, a direct connection, up to about 15-20mA. Depending on what pins you have available, you could parallel-up multiple pins to sink more current, up to a total limit of 100mA. 35mA spread across 2 pins would be a good bet, IMO.