The length of the shortest arc, _s_, between the points

(_x_, _y_, _z_, _t_), and (_ξ_, _η_, _ζ_, _τ_) follows, as in the

sphere, from the equation

cos_s_ (_xξ_ + _yη_ + _zζ_ + _tτ_)

------ = --------------------------- (4.)

_R_ _R_²

One of the co-ordinates may be eliminated from the values given in 2 to

4, by means of equation 1, and the expressions then apply to space of

three dimensions.

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