Mosso worked in the late 19th century, an era that was in retrospect right at the dawn of modern neuroscience. A major question at that time was the relationship between brain function and blood flow.
His early work included studies of the blood pressure in the brains of individuals with skull defects. His most ambitious project, however, was his [Human Circulation Balance] or as he sometimes called it, according to his daughter, his “metal cradle” or “machine to weigh the soul”.
Then again, maybe it wasn’t so strange after all:
A volunteer lay on a table, their head on one side of the scale’s pivot and their feet on the other. It was carefully adjusted so that the two sides were perfectly balanced.
The theory was that if mental activity caused increased brain blood flow, it ought to increase the weight of the head relative to the rest of the body, so that side of the balance would fall.
The scientists reviewing Mosso’s papers aren’t saying one way or another, but later research suggested that the soul weighs about 21 grams.