This profound philosophical argument analyzes the mental processes and opinions of such physicists as Maxwell, Kelvin, Tait, Fourier, Boltzmann, John Herschel, Poisson, Laplace, Joule, Ostwald, Mach, Ampere, Nollet, Coulomb, and Cavendish who, between 1750 and 1900, considered the relationship between mathematics and experience, causing a revolution which questioned the universal applicability of Newtonian "mechanism."