On the use of the viral in Thermodynamics

Abstract

THE ingenious experiment and the deductions from it, described by Mr. S. Tolver Preston in NATURE, vol. xvii. p. 31, throw a flood of light on the subject of availability of heat-energy, which altogether alters the basis upon which the hitherto imperfectly expressed conditions of the use of this form of energy will be made to rest. Mr. Tolver Preston has, in fact, discovered that discriminating “sprite,” or being whom Prof. Clerk-Maxwell imagined (“Theory of Heat,” 1875, p. 328) singling out the fast-moving, and separating them in a space by themselves (without any expenditure of energy), from the slow-moving molecules of a gaseous mass; or what is nearly equivalent to this, he has at least shown how some fast-moving and some slow-moving particles of a mass of gas originally in equilibrium, both as to temperature and pressure, will naturally be so guided amongst each other, that their joint energy will become more available than it was before. But it has, perhaps, not occurred to Mr. Tolver Preston and to some of your readers, that this power or faculty of rendering heat-energy available, which mutual diffusion of heterogeneous gas masses, either through a porous septum or in their own contiguous layers possesses, is a consequence of the general form of efficacy belonging to force, of which Prof. Clausius pointed out the existence in his important propositions on the “virial,” ¹ as he has termed one of the two members, of which this kind of mechanical tendency of force is the sum. The other member of a force's “radiahty” (as it may be termed). “with respect to a given point,” is the vis viva² of the material particle upon which it acts, in a space of which the selected point is the origin. In description of this newly-discovered natural tendency of a force with respect to a given point or focus, it is enough to say that while the statical moment of a force, or the product of the distance of its point of application from a point or fulcrum by the resolved part of the force perpendicular to this distance tends to increase uniformly the moment of momentum (defined similarly with that of force) of the particle upon which it acts, so does the “radiancy” of a force, or the product of the distance of its point of application from a given point or “focus,” together with the vis viva of the particle upon which it acts, tend to increase the “radiancy of momentum” of the particle described in the same way as the radiancy (or the first term of the radiality) of the force, as just defined. We may speak of the radiancies of equal and opposite reactions, or of force-pairs, in the same way that we deal in statics with the moments of couples; with similar general properties of their equilibrium, including the resoluticn of the total radiancy (like the impulse, the horse-power, and the moment) of a system of force, into an internal and an external part with respect to the centre of mass of a material system upon which it acts; and there are principles of conservation of moment and of radiancy of momentum about any point, taken as centre, of all the force-pairs whose moments and radiancies balance each other on a material system. Only the system's vis viva referred to the centre is in the latter case the rate of change of its radiancy of momentum relatively to it. It is in the same way that the conservation of the motion of the centre of mass, and the conservation of energy, are principles of nullity or of inaction of two other forms of force-agency balancing each other on a material system (the impulse of farces, and the product of their impulse by the virtual velocity of their point of application, or their “horse-power”) to which we are obliged to have special recourse to resolve the particular varieties of questions of the “transfer of energy” which occur in mechanics. But it is remarkable that the radiality of a force-pair includes the vis viva of its mass-couplet as one member of its mechanical efficacy, and a surprising example of an agent (evidently the agent of heat-distribution) here presents itself in which vis viva itself is one of the active elements of the mechanical variation or compulsion! Its total tendency in any body acted on internally only by directly reacting force-pairs is the total vis viva, and the sum of the virials of those force-pairs, diminished, if the body is subjected externally to a uniform pressure normal to its surface, by three times the well-known product of this latter pressure by the volume of the bedy (written-3pv).