The Hackwork Coarse- Adjustment. By E. M. Nelson. 259 
whereas contact before this line is called engaging friction, and may- 
be likened to that encountered by a man pushing his stick before him, 
which is altogether a very different matter. The friction at the point 
where the dotted circle and the perpendicular cut one another, when 
the teeth are properly constructed, is roll- 
ing friction, and is very small. 
The dotted circle, which cuts the per- 
pendicular at the point of contact of the 
teeth, is called the pitch circle (tig. 69) ; 
the pitch of the pinion is the breadth of 
a tooth and interspace measured on that 
pitch circle, and the pitch of the rack is 
the width of a tooth and interspace. 
In order that the best results may be 
obtained, the following conditions must be 
satisfied : — 
1. The pitch of the pinion must be the 
same as that of the rack. 
2. The roots of the teeth of the pinion must be hypocycloidal, 
and their points (the addenda, or portions beyond the pitch circle) 
must be epicycloidal. 
3. The roots and addenda of the teeth of the rack must be 
cycloidal. 
4. The diameters of the generating circular rollers of these cy- 
cloids must be the same, and may be equal to half the diameter of 
the pitch circle. (The hypocycloidal portions of the pinion teeth will, 
under this condition, be radii of the pitch circle.) 
5. The pinion should have not less than twelve teeth. 
6. The breadth of the teeth should be 5/11 of their pitch, and 
the width of the space between them 6/11 of their pitch, the back 
lash, or “loss of time,” being therefore 1/11 of the pitch. 
7. Depthing : — The distance from the point of the pinion tooth 
to the bottom of the space in the rack should be 1/10 of the pitch. 
A rack-and-pinion, constructed on the above data, will form as 
perfect a mechanical movement as possible ; but it should be noticed 
that “ loss of time ” is an essential condition of this perfection. If 
involute teeth are used, the pinion would require 25 teeth in order 
to minimise the engaging friction. 
Practice. 
It will be observed, that the sixth condition imposes a “ loss of 
time” equal to 1/11 of the pitch ; now “loss of time” in a coarse- 
adjustment is a veritable nightmare to a microscopist. Most micro- 
scopists care nothing about the mechanical perfection of their coarse- 
adjustments, the sole condition they impose on the maker is, that 
there should be no “ los3 of time.” 
Fig. 69. 
