248 Mr Sang on the adaptation of the Fly-wheel and Pulley 



Excess of the length of Band above 

 circumference of Fly-wheel. 



2696 

 2708 

 2720 

 2733 



2759 

 2772 

 2786 

 2801 

 2816 



2832 

 2849 



2867 

 2886 

 2907 



2929 

 2954 

 2984 

 3020 

 3075 



0.05993 

 0.05548 

 0.05114 

 0.04693 

 0.04284 



0.03888 

 0.03505 

 0.03135 

 0.02780 

 0.02439 



0.02113 

 0.01804 

 0.01512 

 0.01237 

 0.00981 



0.00746 

 0.00534 

 0.00347 

 0.00189 

 0.00067 

 0.00000 



445 

 434 



421 

 409 



396 



38.1' 



370 



355 



341 



326 



309 

 292 

 275 

 256 

 235 



212 

 187 

 158 

 122 

 67 



fi !i 



Having given an account sufficiently clear, as I hope, to be 

 understood by all practical people, of the nature and uses of 

 the preceding Table, I have now to exhibit to such as would 

 examine the matter more deeply, the processes which were used 

 in its formation. 



Let w and p be the diameters of the wheel and pulley, d the 

 difference between them, and 6 the inclination of the free part 

 of the band to the plane of the two axes. 



Then, we have sin d = - ; and the length of each free part of 



the band sj \ — -r- But the length of that portion of the band 

 in contact with the wheel, is ^ (f 4* ^Y and of that in contact 

 with the pulley, p ( ~ — dV The whole length of the band is 

 thus \/ (4 — cP) + K^(| -f ^) +JP(i — ^) '- which is equal ei> 



ther to 



V(4-(?) + 4j-|-<)-i^^; 



