ere so proportioned that the thickness was 1/58th of the
circumference, and the depth 1/375. The side of the beam, supposing it
square, was found by multiplying the diameter of the cylinder by the length
of the stroke, and extracting the cube root of the quotient, which will be
the depth or thickness of the beam. This rule allows a beam 16 feet long to
bend 1/8th of an inch, and a beam 32 feet long to bend 1/4 of an inch. For
cast iron beams the square of the diameter of the cylinder, multiplied by
the length between the centres, is equal to the square of the depth,
multiplied by the thickness.

352. _Q._--What law does the strength of beams and shafts follow?

_A._--In the case of beams subjected to a breaking force, the strength with
any given cohesion of the material will be proportional to the breadth,
multiplied by the square of the depth; and in the case of revolving shafts
exposed to a twisting strain, the strength with any given cohesive power of
the material will be as the cube of the diameter.

353. _Q._--How is the strength of a cast iron shaft to resist torsion
determined?

_A._--Experiments upon the force requisite to twist off cast iron necks
show that if the cube of the diameter of neck in inches be multiplied by
880, the product will be the force of torsion which will twist them off
when acting at 6 inches radius; on this fact the following rule is founded:
To find the diameter of a cast iron fly wheel shaft:--multiply the square
of the diameter of the cylinder in inches, by the length of the crank in
inches, and extract the cube root of the product, which multiply by 0.3025,
and the result will be the proper diameter of the shaft in inches at the
smallest part, when of cast iron.

354. _Q._--What was Mr. Watt's rule for the necks of his crank shafts?

_A._--Taking the pressure on the piston at 12 lbs. pressure on the square
inch, and supposing this force to be applied at one foot radius, divide the
total pressure of the piston reduced to 1 foot of radius by 31.4, and
extract the cube root of the quotient, which is the diameter of the shaft:
or extract the cube root of 13.7 times the number of cubic feet of steam
required to make one revolution, which is also the diameter of the shaft.

355. _Q._--Can you give any rule for the strength of the teeth of wheels?

_A._--To find the proper dimensions for the teeth of a cast iron wheel:--
multiply the diameter of the pitch circle in feet by the number of