In this paper, we compare Maxwell’s formula of the speed of light with the traditional formula and our formula of the speed of light in atomic units, they are c=1/(μ0ε0)^(1/2), cau=1/α and cau=1/(α1α2)^(1/2) respectively. The traditional theory supposes that there is only one α which is the fine-structure constant, but our theory demonstrates that there are two α (α1 and α2) along with their geometric mean αc which could be called the integrated fine-structure constant. Our formula is consistent with Maxwell’s formula essentially, and hence should be reasonable and correct. We present our previous formulas of the fine-structure constant, the speed of light in atomic units and the anomalous magnetic moments of electron, muron and tauon to demonstrate the existence of α1, α2 and αc. We also propose a valuable research topic for mathematical physics to deduce our formula from Maxwell’s formula and provide some reasons for it. As for the fine-structure constant and the anomalous magnetic moment of muon, the relationships between their measured and calculated values are illustrated. In the end, the physical meanings of αc are explained.