OF MILLS. 77 



of cogs in the wheel, and staves in the trundle, are 

 so near the truth for the required purpose, that the 

 least number of revolutions of the mill-stone in a 

 minute is 118, and the greatest number never ex- 

 ceeds 121; which is according to the speed of 

 some of the best mills. 



It is of the greatest consequence to have the 

 teeth of wheels so formed, that the pressure by 

 which one of them urges the other round its axis, 

 be constantly the same. This is by no means the 

 case when the common construction of a spur- 

 wheel, acting in the cvlindrical staves of a lantern, 

 or trundle, is used. The ends of teeth should 

 never be formed of parts of circles, but of a par- 

 ticular curve, called the epicycloid, which is formed 

 by moving the circle D (Fig. 13.) called the 

 generating circle, round the circumference of 

 another circle E, while it turns also round its own 

 centre ; then any point o will describe an epicycloid. 



If a point a (Fig 12.) on the circumference of 

 the circle B, proceed along the plane a C, in a 

 right line, and at the same time revolve round its 

 centre, it will describe a cycloid. 



Emerson observes, that the teeth of wheels 

 ought not to act upon each other before they arrive 

 at the line which joins their centres; and though 

 the inner or under sides of the teeth may be of any 

 form, yet it is better to make both sides alike, which 

 will serve to make the wheels turn backwards. The 

 more teeth that work together, the better; at least, 

 one tooth should always begin before the other has 

 done working. The teeth ought to be so disposed, 

 as not to trouble or hinder one another before they 

 begin to work. 



If the cogs of a wheel and rounds of a trundle 

 could be put in as exactly as the teeth are cut in 



