Page:A Voyage in Space (1913).djvu/66

46 length, the product CS. SK is therefore constant, and it is this property which is used in drawing the straight line; for if K be made to move on a certain circle, C will move on a straight line.

As regards the use for gravity: the pull at P is to the weight W in the same ratio as the tensions in AC and AK.

Now AC is parallel to KB; and thus ALK is the triangle of forces for the point A. The ratio of the tensions is therefore that of KL to KA: or SL to SA, since KS bisects the vertical angle of the triangle: or finally SK to SC, since AC and KL are parallels.

In practice it is convenient to use, instead of the lower string AKB, one just half the length, attached to the middle points of the bars SA, SB: or reduced in any other ratio. The advantage gained is that S need not be so high above the ground.