EARTH'S STUDIES ON BELTING 37 



The centrifugal force in the belt acts radially around the 

 entire circumference, and is balanced by the tension in the 

 two strands of the belt at the extremes of the diameter, 

 as diagrammatically represented in Fig. 6. Each unit of 

 length of the belt will have developed in it a centrifugal force 

 of magnitude/, and acting in the direction shown by the radial 

 arrows. The sum of these unit forces will be the total 

 centrifugal force in the belt, that is 2/=F. The horizontal 

 components of the various forces / are balanced by a force P 

 acting in the opposite direction and which manifests itself 

 as a tension in the belt at the points a and b. The tension 

 T c in each strand is \P. The magnitude of the sum of these 

 horizontal components is the sum of the forces / multiplied 

 by the ratio of the diameter to the length of the semi-cir- 

 cumference along which they act, that is by 2/ir. Therefore 



p _ T _ 2F _ 2 TTWV 2 _ 2WV 2 



Hence 



r,= 



If the weight of a cubic inch of leather belting be taken as 

 sir Ib. and g be put equal to 32^ we have 



rr\ 2 / \ 



which is the formula given by Earth and which agrees sub- 

 stantially with those given by Nagle and Rankine. 



Earth's Theory of Belting. In developing the theory 

 of belting forming the basis of practice in the most pro- 

 gressive shops, which theory accords with the seven require- 

 ments set forth in the first paragraph of this chapter, Mr. 

 Earth found that certain assumptions, formerly held to be 

 true by writers on belting, were, as a matter of fact, falla- 

 cious, and he therefore discarded them. 



The two most important assumptions thus found to be 

 untrue were: (i) The sum of the tensions in the two strands 



