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Rh uniformly, the increase in age is equal to the increase in local time. The advantage of using the age of a particle in forming the equations of motion is that there is a gain in simplicity. The analytical methods based upon the use of the age of a particle may be compared with Lagrange's method of dealing with problems in hydrodynamics, while the methods based on the use of a standard time may be compared with the Eulerian method.

When a particle is moving in an arbitrary manner it is by no means certain that its age can be derived from a knowledge of an initial position and the position at a given time. It is to be expected, in fact, that the age of the particle will depend upon the path from one point to the other, and also upon the rates at which it describes different parts of the path.

There is, at present, considerable uncertainty with regard to the exact laws of the kinematics and dynamics of a body whose motion is not uniform. Systems of non-Newtonian mechanics and kinematics of a rigid electron have been based upon the theory of relativity for the case of uniform motion, but they can hardly be regarded as satisfactory, and difficulties arise as soon as a uniform motion of rotation about an axis is considered.

If mechanics is to be based on the science of electromagnetism, we must make a complete study of the transformations connected with the fundamental equations of electromagnetism.

Now the general problem of determining the transformations which leave the electrodynamical equations unaltered in form, may be partially solved by simply paying attention to the conditions which must be satisfied