hard science vs natural science

hard science

noun
  • Any of the natural and physical sciences that use the scientific method and experiments to test theories. Examples include mathematics, biology, physics, chemistry and geology. 

natural science

noun
  • Any science involved in studying phenomena or laws of the physical world: physics, chemistry, biology, astronomy, and so on. 

How often have the words hard science and natural science occurred in a corpus of books? (source: Google Ngram Viewer )