VI. Lagrange's ballistic problem

Abstract

1. Introduction.—The first part of this paper, written by Love, contains a theoretical solution of the problem of rational hydrodynamics which has been named by writers on ballistics, “Lagrange’s problem”; the second part, written by Pidduck, gives the application to ballistics. In the problem it is supposed that a given mass of gas, which is initially in a uniform state, is contained in a segment of a tube of uniform section. At one end the segment of the tube is bounded by a fixed transverse section, and at the other end the tube is closed by a piston of given mass, which is initially at rest and is free to move along the tube without resistance. It is required to find the subsequent states of the gas and the motion of the piston.