In this article, we give new lower bounds for the size of edge chromatic critical graphs with maximum degrees of \(8\) and \(9\), respectively. Furthermore, it implies that if \(G\) is a graph embeddable in a surface \(S\) with characteristics \(c(S) = -1\) or \(-2\), then \(G\) is class one if maximum degree \(\Delta \geq 8\) or \(9\), respectively.