38 FORCE AND MOTION. 



ant is equal, and opposite to the vertical force which is 

 due to the gravity of V, and this balances the forces repre- 

 sented by AB and AC. Results equally satisfactory will 

 be secured as long as AB : AC :: W : w. 



84. A Substitute. Very satisfactory results may 

 be had by simpler apparatus. Let H 



and K represent two pulleys that work 

 with very little friction. Fix them to a _,,. /t " /i 

 vertical board. The blackboard will " v \/ [/ 

 answer well if the pulleys can be at- 

 tached without injury. Three silk cords 

 are knotted together at ; two of them 

 pass over the pulleys; the three cords 

 carry weights, P, Q, and R, as shown in FIG. n. 



the figure. R must be less than the 

 sum of P and Q. When the apparatus has come to rest, 

 take the points A and B so that AO : BO : : P : Q. Com- 

 plete the parallelogram AOBD by drawing lines upon the 

 vertical board. Draw the diagonal OD. It will be found 

 by measurement that AO : OD : : P : R; or that BO : OD 

 : : Q : R. Either equality of ratios affords the verification 

 sought. 



85. Determination of the Value of the 

 Resultant. With a carefully-constructed diagram (only 

 half of the parallelogram need be actually drawn) the re- 

 sultant may be directly measured and its value ascertained 

 from the scale adopted. The value and direction of the 

 resultant may be found trigonometrically, without actual 

 construction of the diagram, when the angle between the 

 directions of the components is known. In one or two 

 cases, however, the mathematical solution i3 easy without 



