compensating gears is determined as follows:

_r_ + 1
R = -------
_r_

in which

_r_ = _L_ / _l_;
_L_ = lead of spiral;
_l_ = lead of hob thread.

For example, if a hob has a pitch circumference of 3.25, a single thread
of 0.75 inch lead, and 6 spiral flutes, what compensating gears would be
required?

The lead _L_ of the spiral flutes is first determined by dividing the
square of the circumference _C_ of the hob at the pitch line by the lead
_l_ of the hob thread. Thus lead _L_ = _C^2_/_l_, or, in this case, _L_
= 3.25^2/0.75 = 14 inches, approximately. Then _r_ = 14 / 0.75 = 18-2/3.
Inserting these values in the formula for ratio R,

18-2/3 + 1 19-2/3 19-2/3 x 3 59
_R_ = ---------- = ------ = ---------- = --
18-2/3 18-2/3 18-2/3 x 3 56

Hence, the compensating gears will have 56 and 59 teeth, respectively,
the latter being the driver. As the gears for 6 flutes listed on the
regular index plate are, stud-gear 60 teeth, cam-shaft gear 40 teeth,
the entire train of gears would be as follows: Gear on stud, 60;
_driven_ intermediate gear, 56; _driving_ intermediate gear, 59;
cam-shaft gear, 40. It will be understood that the position of the
driving gears or the driven gears can be transposed without affecting
the ratio.

=Classes of Fits Used in Machine Construction.=--In assembling machine
parts it is necessary to have some members fit together tightly, whereas
other parts such as shafts, etc., must be free to move or revolve with
relation to each other. The accuracy required for a fitting varies for
different classes of work. A shaft that revolves in its bearing must be
slightly smaller than the bearing so that there will be room for a film
of lubricant. A crank-pin that must be forced into the crank-disk is
made a little larger in diameter than the hole, to secure a tight fit.
When a very accurate fitting between two cylindrical parts that must be
assembled without pressure is required, the diameter of the inner member
is made as close to the diameter of the outer member as is possible. In
ordinary machine construction, five classes of fits are used, _viz_;
running fit, push fit, driving fit, forced fit and shrinkage fit. The
running fit, as the name implies, is employed when parts must rotate;
the push fit is not sufficiently free to rotate; the other classes
referred to are used for assembling parts that must be held in fixed
positions.

=Forced F