While distributing sth "along" a group is slightly archaic and definitely not common usage, I don't think it's actually wrong...
The perspiration/transpiration thing is very interesting:
I always use transpiration and always thought perspiration was another word for the same thing - maybe a difference between AE and BE...
Turns out I should have paid better attention in biology class...
Transpiration is originally the process of secreting visible moisture via the skin - plus the botany thing.
Perspiration is the evaporation of moisture through the skin which is usually not visible as well as coutaneous respiration. The latter is admittedly not a big thing among humans

Modern usage in English seems to have blurred the distinction quite a bit. Most english sources I found couldn't quite agree on the definition.
But transpiration is definitely the correct word to use here.