Complex sentence: Lord Alverstone told the jury the case was an important one of national interest--though he called "The Shambles of Science" "hysterical"--and advised the jury not to be swayed by arguments on the validity of vivisection.
Split into simpler sentences: Lord Alverstone told the jury the case was an important one of national interest. He called "The Shambles of Science" "hysterical," but advised the jury not to be swayed by arguments about the validity of vivisection.