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



give to the artist the trouble of inspection, would need to exhi- 

 bit the lengths of the bands which would pass over all pulleys 

 and wheels placed at various distances from each other. The 

 inconvenience attending all tables of triple entry, and the exces- 

 sive labour of constructing such a one, forbid the hope of ever 

 seeing it completed. Some mode must be devised which may 

 abridge the labour of the calculator, without adding too much 

 to that of the inspector; and I have now to explain those con' 

 siderations which may be supposed to have led me to that 

 abridgment which I have used : among these will be found all 

 the principles which are necessary to the rightly understanding 

 and using of the subjoined Table. 



When we have a table of the lengths of bands fitting on va- 

 rious wheels and pulleys, placed at one fixed distance from each 

 other, it is not very difficult thence to compute the length of 

 band for any lathe whose axes are placed at a different distance. 

 Conceive all the parts of the lathe last mentioned to be altered 

 in proportion, until the distance between its axes is equal to the 

 distance between the axes of the former, and its parts will be 

 found among those entered in the table. The length of band 

 found for this size has only to be altered in the proper ratio, to 

 give the length wanted, and the same might be said of any other 

 dimension. 



Let the diameters of the wheel and pulley be equally in- 

 creased : a little reflection will satisfy any one that the length of 

 the band, the circumference of the wheel, and the circumference 

 of the pulley will, all three, be equally increased ; and that thus, 

 as long as the difference between the diameters of the wheel and 

 pulley is kept the same, the excess of the band above the circum- 

 ference of the fly-wheel, as well as its excess above the circum- 

 ference of the pulley, is also unchanged. Now it is an easy 

 matter to compute the circumference of a wheel when its dia- 

 meter is known ; so that we require only a table of the excesses 

 of the band above the circumference of the pulley, and above 

 the circumference of the fly-wheel, corresponding to each difle- 

 rence between the diameters of these wheels. 



A table of these excesses, in the formation of which I took 

 every precaution to insure accuracy, is subjoined. The first 



