The fact that the variations which cause the failure of the principle of stationary action---those which violate the symmetry of the particles---are impossible in the actual world is irrelevant. Variations of the track of the particle are equally impossible, since in the actual world a particle cannot move in any other way than that in which it does move. The whole point of the Principle of Stationary Action is to show the relation of an actual state of the world to slightly varied states which cannot occur. Thus the break-down of the principle cannot be excused. But we can see now why it gives correct results in ordinary mechanics, which takes the tracks of the particles as the sole quantities to be varied, and disregards the more general variations of the state of the world for which the principle ceases to be true. \Section{64.}{Retrospect} We have developed the mathematical theory of a continuum of four dimensions in which the points are connected in pairs by an absolute relation called the interval. In order that this theory may not be merely an exercise in pure mathematics, but may be applicable to the actual world, the quantities appearing in the theory must at some point be tied on to the things of experience. In the earlier chapters this was done by identifying the mathematical interval with a quantity which is the result of practical measurement with scales and clocks. In the present chapter this point of contact of theory and experience has passed into the background, and attention has been focussed on another opportunity of making the connection. The quantity $G_{\mu}^{\nu} - \frac{1}{2} g_{\mu}^{\nu}G$ appearing in the theory is, on account of its property of conservation, now identified with matter, or rather with the mechanical abstraction \index{Matter!identification of}% of matter which comprises the measurable properties of mass, momentum and stress sufficing for all mechanical phenomena. By making the connection between mathematical theory and the actual world at this point, we obtain a great lift forward. Having now two points of contact with the physical world, it should become possible to construct a complete cycle of reasoning. There is one chain of pure deduction passing from the mathematical interval to the mathematical energy-tensor. The other chain binds the physical manifestations of the energy-tensor and the interval; it passes from matter as now defined by the energy-tensor to the interval regarded as the result of measurements made with this matter. The discussion of this second chain still lies ahead of us.