The fourth dimension

NOMENCLATURE AND ANALOGIES 145

unknown dimension would come in downwards in the opposite sense to that in which the red line ran before. Now if we use 7, j, &, for the three space directions, i left to right, 7 from near away, k from below up; then, using the colour names for the axes, we have that first of all white runs i, yellow runs J, red runs &; then after

Fig. 89,

the first turning round the & axis, white runs negative j, yellow runs 2, red runs k; thus we have the table :—

z j hk 1st position white yellow red 2nd position yellow white— red

3rd position red yellow white—

Here white with a negative sign after it in the column under j means that white runs in the negative sense of the 7 direction.

We may express the fact in the following way :In the plane there is room for two axes while the body has three. Therefore in the plane we can represent any two. If we want to keep the axis that goes in the unknown dimension always running in the positive sense, then the axis which originally ran in the unknown

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