Transportation on Water 355 



line. Put a dot D on this line to represent the point at which the 

 stick is applied to the wagon. Assume that the stick forms with the 

 base line an angle of 45. Extend the line representing the stick 

 indefinitely. Suppose the scale is a line one fourth inch long for each 

 pound. Measure off the required distance according to the scale on 

 the line representing the stick from the point D. This length is two 

 and one half inches. Take the line just measured as the diagonal of 

 a rectangle and complete the rectangle. Measure a horizontal and a 

 vertical line. Are they equal ? (The values are only approximate in 

 the case of an angle of 45.) Applying the scale to your measurements, 

 how many pounds of force do you find exerted on the vertical line? 

 How many pounds of force are exerted in the downward or wasted 

 effort? How many pounds are effective? What is the total force 

 exerted ? 



Put the stick at a smaller angle with the base line, as for instance 

 at an angle of 15. Extend the line representing the stick in the direc- 

 tion the stick is pushing. Measure off the length to represent the force 

 applied (say ten pounds). Complete the parallelogram. What is the 

 length of the perpendicular to the base? What is the length of the 

 base line of the parallelogram? What amount of force is wasted in 

 the downward push? What amount of force is effective? Why is 

 more force effective in this trial than in the former (B) ? 



Let the angle formed by the stick with the base line be 60. What 

 will be the amount of wasted or ineffective force? What will be the 

 effective force? Make a drawing to scale. 



In what position must the pole be to push the wagon with the least 

 effort or force? Will it form an angle with the ground surface? 

 Will the angle be acute or obtuse ? Explain and illustrate graphically 

 your answers. 



Experimental solution. The important facts may be demonstrated 

 by means of an experiment. In this we shall consider that the putting 

 forces shown on the spring balances are equivalent to the pushing forces 

 represented in the case of the wagon. 



Arrange, as illustrated in Fig. 123, three spring balances just in front 

 of a blackboard or upon a table. Draw a line of indefinite length in 

 continuation of that formed by the string of balance A. Take this as 

 the diagonal of the parallelogram which is to be completed. Draw 

 lines also to represent the strings of balances C and B. 



Now exert upon balance A a pulling force of ten ounces. Record 

 the readings of balances B and C. Measure on the diagonal a length, 

 as P to D, which according to your scale represents the magnitude of 

 the force exerted. Complete the parallelogram by drawing from 



