MECHANICS. $'/> 



' Consult CAMUS on the Teeth of Wheels, Article 557. 

 &c. The curve generated by a point on the surface 

 of a revolving cone, is there called a Spherical Epi- 

 cycloidj as being on the surface of a sphere. Dr 

 BREWSTER, in the Appendix to Fergusons Meclia- 

 nics 9 vol. ii. p. 232. treats of the construction of be- 

 velled wheels. 



a. Toothed wheels are employed in mechanics, not 

 only for increasing or diminishing velocity, so as to 

 adapt a given power to the purpose of producing a 

 certain effect, as in a common mill, where the slow 

 motion of the water-wheel is made to produce the 

 rapid motion of the millstone, but they are also 

 employed for th purpose of producing angular 

 motions, that shall obtain, with great precision, gi- 

 ven ratios to one another. This happens in clock- 

 work, and it is there of importance to determine 

 with accuracy the number of wheels, and the num- 

 ber of teeth ill each. Suppose it is required to 

 make one wheel turn exactly 240 times, while ano- 

 ther turns once : The smaller wheel, which is to 

 turn the fastest, cannot hate fewer than 6 leaves or 

 teeth : The other, therefore, ought to have 6 times 

 240, or 1440> which is more than can conveniently 

 be given to one wheel. Suppose, then, that three 

 wheels ABC, and three pinions b c d, as in figure 9, 

 are to be employed : Then the angular velocity of A 

 is to the angular velocity of b y as 



b x xd to AxBxC, 



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