of the band is about 10 eV for Nb or Nb$_{3}$Sn . Taking r$_{0}$ = 1 . 34 ˚ A , the co-valent radius of Nb gives ( T$_{c}$ )$_{max}$ ≈ 30 K . This is to be compared with the experimental value of 9 . 2 K for Nb and 22 K for Nb$_{3}$Sn . The conclusion is that for the highest T$_{c}$ from electron-phonon interactions, one needs a small mass M of the ion to give the large frequency scale of attractive interactions. In a compound, the electrons near E$_{f}$ must have substantial weight on the same atoms with the small M so that the electron-phonon interactions and the phonon energies are related to the average stiffness W/r 2 $_{0}$. The highest T$_{c}$ of the electron-phonon variety so far is MgB$_{2}$ which satisfies these conditions. Taking the geometric mean of the mass ≈ 13 proton mass and W from band-structure of about 10 eV and r$_{0}$ ≈ 1 ˚ A gives a ( T$_{c}$ )$_{max}$ of about 60 Kelvin while the actual value is 42 kelvin. One cannot do better than metallic Hydrogen where the bandwidth is estimated to be about 1eV. ( T$_{c}$ )$_{max}$ of about 100 K is to be expected. These are generous limits because they exclude the reduction due to the Coulomb pseudo-potential which is expected to be especially severe for hydrogen. An important lesson from the study of the empirical relations in ”high-temperature” superconductors of the e-ph variety and their explanations, is that the parameters deter- mining T$_{c}$ are gross parameters, which depend on the average local stiffness of the lattice and on how the electronic energy of the bands changes with local deformations. Although superconductivity is a fermi-surface phenomena, the parameters determining T$_{c}$ are prop- erties related to the variation of the electronic bonding energy with the local fluctuation responsible for pairing. These lessons carry over to the electronic mechanisms of pairing except that getting effective coupling constants of O (1) with their main benefit - the larger high-frequency cut-offs, requires rather more stringent conditions, as we shall see below. The theory of Fermi-liquids by Landau [48], which was almost concurrent with the BCS theory of superconductivity [1], led to an enormous interest in the experimental study of the properties of liquid He 3 in the 1960’s [49]. Liquid He 3 near the melting line is very strongly correlated with the magnetic susceptibility about 25 times larger than a non-interacting fermi-gas of the same fermi-energy. With BCS theory in mind, it was natural to think of pairing or superfluidity in He $^{3}$. Two He 3 atoms have a large s-wave repulsion due to the IV. SUPERCONDUCTIVITY FROM FERMION INTERACTIONS 31