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On the adaptation f^the Fl^^wheel mid PiiUey of the Turning- 

 iaihe to a given Length of Band. By Mr Ei>wa»d 

 Sang, Teacher of Mathematics, Edinburgh. 



EivBHY one accustomed to the use of the turning-lathe, is 

 aware of the' necessity for frequent changes in the velocity of 

 the spindle. Each different material that is wrought, — each 

 diameter of the various parts of the work,^and almost every 

 different todl that is employed to cut it,— requires a particular 

 velocity. The most ready means for effecting these changes, is 

 to cut two series of grooves, one series in the edge of the fly- 

 wheel, and a corresponding one in that of the pulley ; and to 

 have these grooves so arranged that the same band may fit up- 

 on any one pair of them. 



When the band is crossed^ the formation of these grooves is 

 attended with no difficulty; for, while the sum of the diameters 

 of the wheel and pulley is kept the same, the length of the band 

 is unaltered. We have thus only to increase the diameter of 

 the pulley as much as we diminish that of the fly-wheel ; and it 

 may be noticed, that the same band will pass over any pair of 

 grooves formed agreeably to this rule, whatever be the thick- 

 ness of that band. 



When the band is plain, the arrangement of the grooves is 

 much more troublesome, and needs the aid of calculations too 

 long and too intricate to be performed by the generality of those 

 who are engaged in the construction of turning-lathes ; on this 

 account, the adjustment is most frequently effected after re- 

 peaKed trials. My object is to render these requisite calcula- 

 tions so simple as to offer no serious difficulty to practical men ; 

 for this end, I will avoid every appeal to the complex operations 

 c€ trigonometry, and will use such expressions only as may be 

 mtelligible in the workshop. 



By no artifice can the actual performance of the calculations 

 be avoided ; but, by entering the results in tables, the labour 

 of one person may be made available to others. A complete 

 able, to answer our present purpose, one which would only 



