Before this paper [see Arch. Hist. Exact Sci. 15, 297-383 (1976; Zbl 0359.01019) and Cah. Sémin. Hist. Math. 1980, No.1, 37-50 (1980; Zbl 0449.01004)] the author let know another part of R. Baire’s correspondence (21/1/1874 to 5/7/1932). This time an important collection of letters (50) sent to E. Borel is considered. They belong to the most fruitful period of Baire, that is, 1898-1910. With regard to these letters we can appreciate the efforts and vicissitudes of an active mathematician whose health was bad ever since his early days at the Normal School. The well- documented notes offer a complement view which makes a better understanding of the evolution of the ideas and personal characteristics of R. Baire.