My ohmmeters don't behave as the book "make: electronics" describe
I couldn't find any info for the HP-90EPC, but most of the other meters in the family are only good to 20MegΩ. When I did this on myself with a meter that's accurate to 100MegΩ the resistance did not change with distance. When I put it on the same arm I got 25MegΩ and also about the  same when measuring on opposite hands. 

This is a poor experiment since conductivity of the skin is determined by moisture content (anybody that has had to wear a wrist strap with a conductivity monitor in dry climates can relate). 

The best thing to do to demonstrate resistivity of materials vs distance would be to try a long piece of metal or wire (the thinner the better). The resistivity also needs to be higher than that of the probes (like in the ohms range).