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

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A VOYAGE IN SPACE

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.

 Thus ${\begin{array}{lcl}{\mbox{P}}/{\mbox{W}}&=&{\mbox{SK}}.{\mbox{SC}}/{\mbox{SC}}^{2}\\&=&({\mbox{KA}}^{2}-{\mbox{AS}}^{2})/{\mbox{SC}}^{2}.\end{array}}$ 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. 