8o 



OUR PHYSICAL WORLD 



points of a triangle with sides at least 15 inches long (see Fig. 33). 

 Slip the ring of a spring balance on to each nail. Tie a string 

 to the hook of each spring balance, and then tie the other ends 

 of these strings together, making the tie so that each scale will 

 register some pull. It is evident that the amount registered on 

 any one scale is the resultant of the pulls of the other two. 



The relation between these forces may be graphically cal- 

 culated as follows. Lay a good-sized sheet of paper on the 

 A 



FIG. 33. Diagram of the decomposition of forces 

 GD= i in. Scale A shows i Ib. 

 DE = 4 in. Scale C shows 4 Ib. 

 DF = 3! in. Scale B shows 3! Ib. 



drawing-board underneath the three strings, its center about 

 under the knot. With a ruler draw lines immediately under and 

 parallel to the three strings, the three lines meeting immediately 

 under the central knot (D in the figure). Suppose the scale at 

 A measures i pound, the scale at C, 4 pounds. Lay off on line 

 DG i inch, on line DE, 4 inches. From point G, i inch from D, 

 draw a line parallel to DE, and from point E, 4 inches from D, 

 a line parallel to DG, thus making a parallelogram. Continue 

 the line BD, and it will make a diagonal of the parallelogram. 

 Its length in inches will be the pull on the scale at B in pounds. 



