、。
My experimental method showed a different spirit from this one.
Literal
I [of-の] experiment method [topic-は], this [from-とは] different spirit [object-を] was-showing.
A slightly literary sentence from what sounds like a scientific or philosophical essay. 精神 ('spirit, mindset, essence') is used here metaphorically to mean the underlying philosophy or attitude of the method, not a literal 'spirit.' これとは違う ('different from this') is the standard comparison pattern. 示していた is past progressive of 示す ('to show, to indicate').