242 Mr Sang on ike adaptation of the Fly-xvheel and Pidley 



with this number, the first column of the table. The nearest 

 number which we can find is 0.75, opposite to which, in the se- 

 cond column, is found 3.32044. To correct this for the re- 

 maining figures 333, we multiply by these the tabular difie- 

 rence 1958, cutting off as many figures from the right of the 

 product as there are figures in the multiplier: this done, we ob- 

 tain the correction 653, which, added to 3.32044, gives 3.32697 

 for the correct excess of the band above the circumference of 

 the pulley. But, if we multiply 3.1415926 by .08, the diame- 

 ter of the pulley, we have .25133 for its circumference ; so that 

 the whole length of the band, the sum of 3.32697 and .25133, 

 must be 3.57830. 



In order to compute the size of the new groove to be cut in 

 the wheel, we observe, that, as the band now passes over a pul- 

 ley whose diameter is 0.16666, its excess above the circumfe- 

 rence of that pulley, which circumference is .52360, is 3.05470. 

 Entering the second column of the table in search of this num- 

 ber, and taking that which is immediately Z^^^, we find 3.05195, 

 which has 0.61 opposite to it in the first column ; to obtain the 

 correction for this number, we divide 275, the error, by 1884, 

 the tabular difference, afiixing as many ciphers to 275 as we 

 wish to obtain new decimal places : the result of this division is 

 146, whence the true difference between the diameters of the 

 fly-wheel and pulley is 0.61146; but the diameter of the pul- 

 ley is 0.16667, wherefore that of the fly-wheel is 0.77813. 



These two results, multiplied by 30, give, for the length of 

 the band, 107.349 inches ; for the diameter of the new groove, 

 23.344 mches. 



II. The distance between the axes of a turning-lathe being 

 32 inches ; and two grooves on the fly-wheel having 38 and 34 

 inches for their diameters : the lesser groove on the pulley is 

 to be 3 inches in diameter ; required the size of the other ? 



Dividing all the dimensions by 32, we obtain, for the diame- 

 ters f]^^^ wheels 1.1 8T5 and 1.0625, and for that of the lesser 

 groove on the putt^y .09675. 



Entering the lirst col<umm of the table fer 11.09375, whick is 

 the drflfeifnce between the diameters of the first pair of grooves, 



