OF MILLS. 79 



parts, as 1, 2, 3, 4, 5, in the cog C; allow three 

 for the bottom to the pitch-line of the cog; the 

 other two parts for epicycloid, so as to fit and bear 

 on the stave equally. The mill-\v rights in general 

 put the point of a pair of compasses in the dot 3 of 

 the cog a, and strike the line d e ; then remove 

 the point of the compasses to the point d, and 

 strike the curve line 3 f, which they account near 

 enough the figure of the epicycloid. 



The method for a face-wheel is thus: divide the 

 pitch-line A B (Fig. 2.) into the number of cogs 

 intended, as a b c ; divide the distance b c, into 

 seven equal parts: allow three of those parts for 

 the thickness of the cogs, as 1, 2, 3, in the cog a, 

 four for the height, and four for the width, as d e, 

 and four for the thickness of the stave m; draw a 

 line through the centre of the cog, as the line A I, 

 at S; and on the point 5, describe the- line d e; 

 remove the compasses to the point A, and draw the 

 line fg, which forms the shape of the cog; then 

 shape the cog on the sides to a cycloid, as d efg 

 (Fig. 1.) But this method of setting out the 

 shape of a cog is variable, according to the cycloid 

 in different diameters of wheels. 



In common spur-nuts, divide the pitch-line A 

 into twice as many equal parts as you intend teeth, 

 as a, b, c, d, e (Fig 3.); with a pair of compasses 

 opened to half the distance of any of those divi- 

 sions, from the points a 1, c 3, e 5, draw the semi- 

 circles a, c, and e, which will form the ends of the 

 teeth. From the points 2, 4, and 6, draw the semi- 

 circles g h i, which will form the hollow curves 

 for the spaces; but if the ends of the teeth were 

 epicycloids instead of semicircles, they would act 

 much better. 



