Passive Total Systems with Constant Coefficients.

where YO has arbitrary constants for elements. T.he system composed of (1) and (3), if passive, is known to have a unique solution in the set of analytic functions by a general theorem of Konig1 and the linearity of the right members makes possible the immediate extension of this result to the set of once differentiable functions (say, by the method of successive approximations). Recently, Vessiot,2 Saltykow3 and Pini4 have proved that the solution of a passive system (1)-or rather the system (1) in which Y has a single column, a system essentially equivalent although perhaps less easy to treat-can be expressed in finite form by means of the elementary functions. The first two mentioned authors place restrictions upon the characteristic roots of the matrices and the characteristic roots play prominentroles in the discussions of all three. It is the purpose of this note to point out firstly, that K6nig's method of solution and elementary integration applied directly to the system (1), (3) for which (2) is satisfied give