38 



LEATHER BELTING 



of a running belt is constant under any variations in the effect- 

 ive pull. (2) The coefficient of friction between the belt 

 and its pulley is constant for any given set of conditions, 

 irrespective of the velocity of the belt. In place of the 

 first of these two erroneous suppositions, Mr. Barth enun- 

 ciated and proved the following theorem : Under any variation 

 in the effective pull of a belt, the sum of the square roots of the 

 tensions in the two strands remains constant. 



Coefficient of Friciio::. To take the place of the theory 

 of a constant coefficient of friction, Mr. Barth derived the 

 empirical formula (2), given on page 35, which gives an 

 increased value to the coefficient with increasing velocity 

 of the belt. The formula gives a value which ranges from 

 0.26 at zero velocity to 0.52 at a belt velocity of 6500 ft. 

 per minute. The value of the coefficient of friction as given 

 by Morin in his experiments was, for oily belts 0.15; for 

 greasy belts, 0.23; for wet belts, 0.36, and for dry belts, o 56. 

 Messrs. Towne and Briggs in their experiments in 1868 rec- 

 ommended the value of 0.42 as expressing an average of the 

 conditions of belt operation, while Releaux recommended 

 0.25. The values of the coefficient of friction, according to 

 formula (2), are given in the table below: 



VALUES OF THE COEFFICIENT OF FRICTION OF LEATHER 

 BELTS IN IRON PULLEYS. (EARTH'S FORMULA.) 



It will be observed that these values are within the range 

 given by tne experimenters whose work is noted above. 

 While the formula is not claimed to give values that are exact 



