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On a method ofBcgistering the Force actually transmitted through 

 a Driving-Beit. By Edward Sang, Esq., F.R.SS.A., Pro- 

 fessor of Civil Engineering, College, Manchester. Com- 

 municated by the Royal Scottish Society of Arts.* 



It is a desideratum to have the means of ascertaining how 

 much force is actually consumed in the working of a machine. 

 Whenever the motion is communicated by the intervention of 

 a belt or band, this can be very easily accomplished. 



When we see a belt passed over two pulleys, and look with- 

 out any narrow examination at the motion, we regard the ac- 

 tion as a very simple one ; there is more in it, however,- than 

 appears at first sight. For the sake of clearness, let us call 

 the driving-pulley the drum, and the other the pulley. The belt 

 passed over them, whether plain or crossed, has two free parts, 

 one of which draivs and the other of \y\x\ch. follo?vs. If it were 

 possible that no force were needed to turn the pulley, these 

 tv/o free parts would be in the same state of tension ; but 

 whenever any resistance is made to the motion of the pulley, 

 the drawing part is distended more, and the following part less, 

 than usual ; and experiments show, that, within all practical 

 limits, this change is exactly proportional to the pressure ne- 

 cessary for overcoming the resistance. 



As the movement proceeds, the distended part of the belt 

 is lapped over the drum, and, so to speak, the contracted part 

 is lapped over the pulley, so that the circumference of the 

 drum moves more swiftly than that of the pulley ; thus, if the 

 distension be 1 in 100, for 100 inches of the drum there would 

 only be 99 inches of the pulley passed over. 



The difference between the velocity of the drum and that 

 of the pulley thus indicates the pressure needed to carry the 

 drum round. Now, this pressure, combined with the distance 

 through ^vhich it acts, gives the force used ; and hence, the 

 simple difference between the distances passed over by the 

 circumference of the drum and by that of the pulley is exactly 



* Eead before the Royal Scottish Society of Arts 9th January 1843. 

 VOL. XXXIV. NO. LXVIII. APRIL 1843. s 



