Polytechnic Association. 823 



be no centrifugal force exerted upon the arm, C D ; and yet, should 

 C D offer resistance to revolution, say hy friction on the center or 

 otherwise, force would be transmitted from A, through A C, to C; 

 and the living force of the mass A would, in time, be exhausted in 

 performing work at D. 



Supposing, also, that when A and C are on the line of the centers 

 13 and D, the cohesion of the crank A B should be suddenly destroyed, 

 there is no doubt that the total amount of the centrifugal force of A 

 would be exerted at C, on the arm C D, and in the line of that arm. 

 Also, when the two arms are in the position perpendicular to the 

 line of the centers, there will be no radial stress exerted upon C D, 

 but the whole living force of A will act at C in a direction normal 

 to the arm; so that if the resistance at C should be sufficient, this 

 force might be wholly absorbed, and the motion arrested in a space of 

 time inappreciably small 



At any position later in the revolution, such as is represented m 

 Figure 2, the centrifugal force of the mass A, acting in the direction 

 of the radius B A, acts only partially at C. Taking A E, on the radius 

 B A produced, to represent this force, and resolving into the compo- 

 nents A F and F E, it is A F only which acts on C D, and this not 

 altogether radially."" Take C I, on the line connecting A 'and C, equal 

 to A F, and draw I K perpendicular to C D produced. C I repre- 

 sents the component of the centrifugal force of A acting at C ; and 

 C K represents the element of this component, which acts in the 

 direction of the radius D C. 



If, now, the revolution be supposed to begin from O, and the are 

 of revolution O A, be represented by <p, then A F will be equal to 

 A E cos <p, and C K will be equal to C F cos <p= A F cos <p =A E cosV 

 Hence the radial force exerted upon C D will be, to the centrifugal 

 force of the body revolving at A, as radius is to the square of the 

 cosine of the arc passed over from zero taken at the line joining the 

 centers. The radial force on the arm or crank, C D, is, therefore, 

 never equal to the centrifugal force of the revolving body, except at 

 the moment when cos? = radius; or when <p = 0° or 180°. 



