34 FORCE AND MOTION. 



or sugar refinery, difference between polar and equatorial 

 weights of a given mass, etc. 



77. Note. Mathematical formulae for measuring the force 

 necessary to overcome this tendency of matter to move away from 

 the centre around which it may be revolving, or, as it is generally 

 expressed, for measuring the centrifugal force, may be found in the 

 Appendix. It is sufficient here to mention that this force varies 

 directly as the mass and as the square of the velocity, the radius 

 remaining the same ; doubling the mass doubles the force needed, 

 but doubling the velocity quadruples the needed restraining force. 



78. The Second Law. The second law of motion 

 is sometimes given as follows: A given force will pro- 

 duce the same effect whether the body on which it 

 acts is in motion or at rest ; whether it is acted on 

 by that force alone or by others at the same time. 



(a. ) Many attempts have been made to show that these are only 

 two ways of stating the same proposition ; most of them are more 

 perplexing than profitable. In the law as given by Newton ( 72), 

 the word motion is doubtless used in the sense of momentum. If the 

 substitution of " momentum " for " motion " makes the reconciliation 

 any easier, no objection can be made to the substitution. 



79. Resultant Motion. Motion produced by 

 the joint action of two or more forces is called 

 resultant motion. 



The point of application, direction, and magnitude of 

 each of the acting forces being given, the direction and 

 magnitude of the resultant force are found by a method 

 known as the composition of forces. 



80. Composition of Forces. Under composi- 

 tion of forces, three cases may arise : 



(1.) Wlien the given forces act in the same direc- 

 tion. The resultant is then the sum of the given 

 forces. Example : Rowing a boat down stream. 



