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1. The present paper is suggested by that of Dr. H. F. Baker in the ‘Proceedings of the London Mathematical Society,’ vol. xxxv., p. 333, “On the Integration of Linear Differential Equations.” In that paper a linear ordinary differential equation of ordern is considered as derived from a system ofn linear simultaneous differential equationsdx i /dt =u i1x ++u in x n (i = 1...n ), or, in abbreviated notation,dx /dt =ux , whereu is a square matrix ofn rows and columns whose elements are functions oft , andx denotes a column ofn independent variables. A symbolic solution of this system is there given and denoted by the symbol Ω(u ). This is a matrix ofn rows and columns formed fromu as follows :—Q (ϕ ) is the matrix of which each element is thet -integral fromt 0 tot of the corresponding element ofϕ ,ϕ being any matrix ofn rows and columns; then Ω(u ) = 1+Qu +Qu Qu +Qu Qu Qu ad inf ., where the operator Q affects the whole of the part following it in any term.

info geting lost in plates 7u,8,9,11 and 13 - I. On the normal series satisfying linear differential equations