λ = N (0) < I 2 > / ( M < ω 2 > ) ∝ 1 + N (0) W (28) ( T$_{c}$ )$_{max}$ ≈ √ E$_{c}$ 2 Mr 2 0 exp( − 3 / 2) . (29) One may estimate the magnitude for compounds with Nb as the main element with atomic mass 92. The typical cohesive energy per formula unit estimated from the second moment Using the expression, T$_{c}$ ≈ < ω > exp − (1 + λ ) /λ , and assuming < ω > ≈ < ω 2 > 1 / $^{2}$, one can use the two empirical relations to express T$_{c}$ in terms of λ, E$_{c}$/r 2 0 and the ion mass M . Now maximizing T$_{c}$ with respect to λ gives that the optimal value of λ ≈ 2 and It is an amusing excercise to use the empirical relations to see the scale of maximum T$_{c}$ . Such an excercise was indulged by McMillan [25] and by Anderson and Cohen [16] for pseudopotential metals with amusing misunderstandings resulting, for which the originators can hardly be blamed. The emphasis in these estimates was both on conditions on lattice stability and the compeition between the repulsive Coulomb pseudopotential and the at- tractive interaction through phonons. I give here an estimate for maximum T$_{c}$ based on the empirical relations discussed above, which is similar to that done about 30 years ago [15]. This is valid for metals and compounds where a tight-binding approach to the electronic structure and electron-vibrational interaction is valid. These are the likely materials for the highest T$_{c}$ by e-ph. This is in qualitative accord with the data in Fig. (6); the 3d, 4d and 5d metals have progressively larger band-widths and the anti-bonding part of the band has effectively a larger band-width than the bonding part. constant. For transition metals and alloys this is exhibited in fig. (6). Only the first half of the 3d metals is superconducting; for 4d and 5d metals the two lines correspond to the fermi-level in the bonding part of the band and in the anti-bonding part of the band. This ”constancy” with a different value is also followed in the A-15 family of superconductors [47]. This rule may also be derived within the tight-binding approximation [15] and is summarized in the appendix.The final result is that for N (0) W >> 1, where W is the electronic bandwidth 1. Maximum T$_{c}$ and General Lessons. 30