EARTH'S STUDIES ON BEL*TING 41 



in either strand of the belt; that is, the effective tension in 

 the tight strand is (ht c } and in the slack strand (fe 0- 

 The total friction of the belt on the pulley is the ratio of the 

 effective tensions. It has previously been shown that this 

 ratio which is the tractive or driving force of the belt on the 

 pulley, is 



?iZ^ = e *. (6) 



/2-/c 



In order to make use of the common system of logarithms, 

 instead of the Naperian system, and to obtain values of a in 

 degrees instead of radians, both of which will be found more 

 convenient, the expression io- 00758/e may be substituted for 

 the expression e fa , 6 being taken in degrees. That is, the 

 ratio of the effective tensions is the number whose common 

 logarithm is 0.00758/0. 



To obtain values of /, we may use the empirical formula 



The centrifugal tension developed at any velocity we have 

 already found to be 



t c = 0.00000345472 (3) 



While a formula has been developed for obtaining directly 

 the value of t\, it is here only of academic interest, because of 

 the fact that we can, by combining formulae (2), (3), (4), (5) 

 and (6), obtain a formula expressing the value of p in terms 

 of /, a, A and V. As the value of p must in any case be 

 determined, and as from it the values of t\ and ^2 can then 

 be ascertained, if desired, by much simpler formulae it is 

 unnecessary to consider here the fundamental formula for t\. 

 Combining the above mentioned formulae we obtain 



(e fa i) (2^4 0.00001036 F 2 ) , s 



P- 2e f. +I - (7) 



which can be converted, by the substitution of the expression 

 given above for e fa to 



