on £ n : x0w = ^, ^in, • • • , xnn = b, where the asterisk indicates a function defined on En (replacing the bold-face type in my former paper), *f(r) = *f(xrn) and A*/(r) = */(r + l ) * / ( r ) , every solution of this system goes over in the limit as n, the number of points in Eny becomes infinite, in such away t h a t X is completely^ subdivided to the corresponding solution, that is, the solution having the same initial values at x = a, of the differential system (1). The present paper shows that the conclusions of our former paper, stated above, are valid for all possible methods of defining the coefficients of system (2), so long as limn.*oo*^4;y(£) =Au(x), limn^oo*&(£) =]8i(ac), almost everywhere on X, and there exists a summable function G(x) on X such that \*Au(p) |, |*&(£) I <G(x) for all n, (i,j = \, • • ,m),on Ipn:xpn?ix^Xp+i,n, where p varies with n in such a way that the point x belongs to Ipn. It shows further that the approach to the limit is uniform on X and that all of these conclusions are valid for any law of complete subdivision of X by the points of En. Our former paper indicated ready adaptations of the work to non-