Page:Eddington A. Space Time and Gravitation. 1920.djvu/116

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100
THE NEW LAW OF GRAVITATION
[CH.

intervals in their correct proportions. Our natural picture of space-time takes and as horizontal and vertical distances, e.g. when we plot the graph of the motion of a particle; but in a true map, representing the intervals in their proper proportions, the and lines run obliquely or in curves across the map.

The instructions for drawing latitude and longitude lines (, ) on a map, are summed up in the formula for , p. 79,

and similarly the instructions for drawing the and lines are given by the formula (7).

The map is shown in Fig. 14. It is not difficult to see why the -lines converge to the left of the diagram. The factor decreases towards the left where is small; and consequently any change of corresponds to a shorter interval, and must be represented in the map by a shorter distance on the left. It is less easy to see why the -lines take the courses shown; by analogy with latitude and longitude we might expect them to be curved the other way. But we discussed in Chapter iii how