is not a vector but a tensor. On account of their skew-symmetrical character there are not nine, but only three independent equations of this system. The possibility of replacing skew-symmetrical tensors of the second rank in space of three dimensions by vectors depends upon the formation of the vector
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If we multiply the skew-symmetrical tensor of rank 2 by the special skew-symmetrical tensor introduced above, and contract twice, a vector results whose components are numerically equal to those of the tensor. These are the so-called axial vectors which transform differently, from a right-handed system to a left-handed system, from the . There is a gain in picturesqueness in regarding a skew-symmetrical tensor of rank 2 as a vector in space of three dimensions, but it does not represent the exact nature of the corresponding quantity so well as considering it a tensor.
We consider next the equations of motion of a continuous medium. Let be the density, the velocity components considered as functions of the co-ordinates and the time, the volume forces per unit of mass, and the stresses upon a surface perpendicular to the -axis in the direction of increasing . Then the equations of motion are, by Newton's law,
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in which is the acceleration of the particle which at