energy, we may regard them as preserving their identity when the bodies approach, and as being absorbed by the moving bodies, so that their potential energy is converted into kinetic. A conductor moves in such a way that the absorbed energy is a maximum. Fig. 1 also illustrates the rotation of the energy-cell as the particles approach. If on any one of the energy-paths, as for instance (7), the direction of the line of force (indicated by a dotted line) cutting it at different points be noticed, it will be seen that this direction constantly changes as the particles approach, so that the tangent to the line of force rotates about the point of intersection. The velocity of the different energy-cells is indicated by crosses along the curves, at such points that, when the two particles come together from an infinite distance apart, the cells move from cross to cross in equal intervals of time. The same time is taken in moving from the cross marked 10 to the origin. 5. In fig. 2 the paths of the energy-cells are shown when two equal like particles repel one another. It will be noticed that, as the particles move apart, the energy in each half of the field follows the motion of the particle in that half, and at the same time moves nearer to the central line. It is clear that the result will be that energy will flow from the dielectric into the particle as it moves away, and being lost as potential energy will reappear as energy of motion. Even when the particles are an infinite distance apart there will still be a number of energy-cells in the æther, that is, the particles will still possess potential energy. This is explained by supposing that every polarization tube must begin and end somewhere. In this case we may suppose that though A and B are an infinite distance apart, the negative particle C is again an infinite distance beyond A, and the negative particle D an infinite distance beyond B, so that the tubes from A end in C, and those from B in D. Then, after B and A have been repelled to a great distance from one another and all the potential energy due to their original nearness has been exhausted, there will still remain the energy due to the separation of D from B and of A from C. e 6. If H, is the intensity of the electrostatic field, or the force acting upon a particle with unit charge; e B. the number of tubes of induction per sq. centim., or the induction in the direction of the line of force; D, the number of polarization tubes per sq. centim., or the polarization or displacement in the same direction; : K the dielectric constant of the medium; The volume of an energy-cell is proportional to the square of its length measured along a line of force. Figs. 1 and 2 show how in general the portion of the line of force intercepted between two equipotential surfaces diminishes as the movement proceeds. The volume of the energy-cell constantly tends to diminish, though in some cases, as in fig. 2, the volume of some of the cells has to increase for a while to allow the rest to contract. During this contraction the length of the cell bears to its area the constant ratio K It has seemed worth while to trace roughly the curves of equal energy-density in the æther about equal unlike and equal like particles. These are shown in figs 3 and 4. The numbers apply to masses of 100 with a distance 10 between them. 7. Maxwell has discussed (Scientific Papers, vol. i. pp. 570571) the modifications which must be made in the theory to make it fit in with the observed facts of gravitation. The energy diagram for two gravitational particles is the same as that for two like electrified particles. The polarization tubes go off to infinity, and do not, as far as we know, end on negative gravitational matter. The properties of the cells between the polarization tubes and the equipotential surfaces are exactly opposite in the two cases of electricity and gravitation. The electrical energy-cells are constantly tending to contract both in length and section, but so that the area of the section always bears a constant ratio to the length of the cell. The gravitational energy-cells, on the other hand, constantly Fig. 3. tend to expand, the same ratio holding between area and length as in the former case. While each electrical cell contains according to Maxwell's theory half a unit of energy, the gravitational cells must be supposed to contain half a unit less of energy than the same volume of undisturbed æther. The gravitational cells are negative energy-cells. This expansion of the negative energy-cells implies a kind of contraction of the energy of the gravitational æther. In the case of electricity the final state is reached when the energydensity is every where zero, all the energy having passed into the particles; in the case of gravitation when the density is uniform over a series of concentric shells, being a maximum at an infinite distance from ponderable matter. 8. Fig. 2 shows the path of the negative energy-cells, when two equal gravitational particles come together from an infinite distance apart. It can be seen that the cells retreat from the particles as these approach one another. There will be a greater number of negative cells in the æther when the particles are in contact than when they are at a distance. This is merely another way of saying that (positive) energy has passed from the æther into the particles. The instantaneous position of the lines of energy-flow, for a given position of the moving gravitational particles, is something like fig. 2, the motion being away from the median plane and towards the line joining the two particles. The flow of energy is on the whole in the direction opposite to the motion of the particle. The potential energy absorbed by two gravitational particles, when they fall together, comes from the space between them. The increase in the number of negative energy-cells, when two gravitating masses approach, is equal to twice the gain in kinetic, or loss in potential energy. The proof is the same as in the case of static electricity, due regard being paid to the signs of the quantities involved. Thus the theory may be advanced that each of these nega tive energy-cells contains half a unit less of energy than the same volume of æther in which no such cells exist. An increase in number of these cells corresponds to a flow of energy from the gravitational æther into matter, where it is converted into kinetic energy. Some difficulty may arise in special cases on account of the fact that in the case of gravitation the attracting mass has a volume distribution, instead of being confined to a surface like static electricity on a conductor. Each unit mass sends out a tube of polarization, whether it is on the surface or not, and a considerable proportion of the energycells exist inside the surface. In the case of a single homogeneous sphere, at a distance from all other bodies, one sixth of the negative energy-cells are within the surface. It is clear, then, that in general the energy is not removed |