30 JUNIOR GRADE SCIENCE 



By comparing columns 4 and 5 it will be seen that the three downward 

 forces -A, B, and C, acting upon the lath, are kept in equilibrium by one 

 upward force R. 



(b) Hang the two weights B and C together from the middle of the lath 

 suspended from the spring balance. Notice that the reading of the balance 

 is the same as when the two weights are hung from the ends of the lath. 



Parallel forces. It has been seen that the earth exerts a downward 

 pull upon all objects on its surface, and that in consequence of this 

 all things fall to the ground if unsupported. It follows, therefore, that 

 every mass which is supported above the earth's surface is constantly 

 being pulled downwards, even though it does not fall. If a beam, 

 for instance, is supported horizontally by resting the ends upon two 

 posts, each particle of it may be regarded as being pulled earthwards 

 by an attractive force. The direction of the pull is everywhere towards 

 the centre of the earth, so for any one spot on the earth's surface we 

 may consider the attractive forces due to gravity to be parallel to one 

 another. 



When a stiff lath or rod of uniform thickness rests upon two letter 

 balances or is supported by hanging each end from a spring balance, 

 the experiment represents on a small scale the case of a beam referred 

 to before ; and by using spring balances it can be proved that the 

 weight supported at its ends is equally divided between the two supports. 

 In other words, the two upward forces exerted by the balances are 

 together equal to the downward force represented by the weight of 

 the beam. 



If a load be placed anywhere upon the lath, the balances still show 

 that when the lath is in equilibrium the sum of the upward forces is 

 equal to the sum of the downward forces. 



Principle of parallel forces. The principle of parallel forces 

 demonstrated by the experiments referred to may now be definitely 

 expressed as follows : The resultant of a number of parallel forces is 

 numerically equal to the sum of those which act in one direction, less the 

 sum of those which act in the opposite direction. In other words, the 

 resultant is equal to the algebraic sum of the forces. 



If two equal parallel forces act in the same direction upon a body, 

 the total force will be obtained (as might be expected) by adding the 

 two individual forces together. In like manner, if two unequal parallel 

 forces act in opposite directions the net effect can be found by subtract- 

 ing the smaller of the two forces from the greater ; the direction of 

 the resultant is that of the greater force. 



