of the Turning4athe to a given Length of Band. 241 



column contains the differences between the diameters of the 

 fly-wheel and pulley, estimated in decimal parts of the distance 

 between their axes, which is, throughout, regarded as the tmit. 

 In the second column, are inserted the corresponding excesses 

 of the length of the band above that of the circumference of the 

 pulley ; these excesses being, for the sake of interpolation, ac- 

 companied by their differences. And the third column exhibits 

 the excesses of the length of the band above the circumference 

 of the fly-wheel, with their differences. The numbers in the 

 first and second columns go on increasing, but those in the third 

 column decrease. 



All the dimensions of any turning-lathe must be divided by 

 the number which expresses the distance between the axes, be- 

 fore any of them can be sought for in this table ; and the results 

 obtained from the table must again be multiplied by the number 

 formerly used as a divisor, in order to obtain the quantities 

 sought for. But this calculation may be avoided, by forming 

 a scale of the tenth, hundredth and thousandth parts of the 

 distance between the axes, and by using this scale in all the 

 measurements. The latter method will, in all probability, be 

 found the most convenient. As examples of the use of the 

 Table, I will propose two questions. 



I. On the pulley of a turning-lathe are already two grooves, 

 one of 2.4, and the other of 5.0 inches diameter. The centre 

 of the fly-wheel is distant 30 inches from that of the pulley, and 

 the larger groove to be made on the fly is 25 inches in diame- 

 ter. Required the diameter of the other groove to be made on 

 the wheel ? 



Dividing all these dimensions by SO, we obtain unit for the 

 distance between the axes, which is the distance assumed in the 

 table ; 0.08 for the diameter of the lesser, 0.1666 for that of the 

 greater groove on the pulley, and 0.8S3 for that of the greater 

 groove on the fly-wheel. 



These numbers are just what would have been found on 

 taking the dimensions with the scale above described. 



In order to find the length of the band, we take the diffe- 

 rence between 0.8333 and 0.08, which is 0.75333, and enter. 



