compare the times for the straight segments QP′ and Q′P′, that is we have only to compare the lengths of these segments. Now clearly from the point P′ on a normal QP′ to a surface S of double curvatures, P′Q is the line of least length that can be drawn to meet the surface in the neighbourhood of Q, so long as the centres of both the principal curvatures at Q are beyond P′; it is the line of greatest length when P′ is beyond both these centres; and it is only of stationary length, neither maximum nor minimum, when P′ is between these centres.
21. Let us consider the form that these principles will assume when the matter across which the radiation is travellingis itself in motion. The radiation is now not reversible, and the demonstration of the law of ray-direction must be expressed differently from the above. This however is easily done.
The time from O to Q is the same as from O to Q′, hence is the same as from O′ to Q, where OO′ is equal and parallel to QQ′,
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each of them being infinitesimal compared with OQ. Hence the disturbances from all points O′, near on the plane wave-front, reach Q at the same time and therefore in common phase, and therefore accumulate, while at a point in any direction other than OQ they would annul each other. Thus the path of a ray is still determined by the principle of stationary time: but the path from P to P′ is not the same as the path from P′ to P because the velocity of propagation relative to absolute space is altered on reversing the direction of the ray.
In circumstances of moving matter there are moreover two kinds of rays to be distinguished, one of them being the paths of the radiant energy with respect to the particles of the moving matter, the other the absolute paths of the radiant energy in the stagnant aether, or as we may say in space. As radiation is revealed to us wholly by its action on matter, including therein the parts of the eye itself, it is the former
