of the Turning-lathe to a given Length of Band. 243 



we find in the third column, opposite 1.09, the number 0.59297 : 

 To correct for the remaining figures, multiply 992, the tabular 

 difference, by 375, and cut off" three places ; these operations 

 give S72, which has to be subtracted from 0.59297, because 

 the numbers in the third column grow less. The true excess 

 of the band above the drcumference of the wheel, is thus 

 0.58925. But the diameter of the wheel is 1.1875, therefore 

 its circumference is 3.73064, and the whole length of the band 

 4.31989. 



The circumference of the second groove on the fly-wheel is 

 3.33794, wherefore the excess of the band above that circum- 

 ference is 0.98195. Entering the third column for this num- 

 ber, and taking the one immediately greater^ we find, opposite 

 to 0.98809, 0.73 in the first column. Dividing the error 614 

 by 1195, the tabular difference, we obtain 514, which, annexed 

 to 0.73, gives 0.73514 for the true difference between the dia- 

 meters. But the diameter of the wheel is 1.0625; wherefore 

 that of the pulley is .32736. 



These results, multiplied by 32, give. 



For the length of the Band, 13a2365 inches. 



For the diameter of the New Groove, 10.4755 inches. 



If it be wished to allow for the thickness of the band, we 

 bave only to add to the calculated lengths, the circumference of 

 ^ circle which has the thickness of the band for its diameter : 

 the diameters of the grooves will be in no way aff*ect€d by it. 



With regard to the accuracy of the calculations, it may be 

 mentioned, that there is no probability of an error of the thou- 

 sandth part of an inch in any of the diameters. To this de^ 

 gree of exactness few will pretend to work. 



