A.—­The method of computation will be as follows:—­to find the dimensions of a malleable iron paddle shaft, so that the strain shall not exceed 5/6ths of the elastic force, or 5/6ths of the force iron is capable of withstanding without permanent derangement of structure, which in tensile strains is taken at 17,800 lbs. per square inch:  multiply the pressure in lbs. per square inch on the piston by the square of the diameter of the cylinder in inches, and the length of the crank in inches, and extract the cube root of the product, which, multiplied by 0.08264, will be the diameter of the paddle shaft journal in inches when of malleable iron, whatever the pressure of the steam may be.  The length of the paddle shaft journal should be 1-1/4 times the diameter; and the diameter of the part where the crank is put on is often made equal to the diameter over the collars of the journal or bearing.

364. Q.—­How do you find the diameter of the crank pin?

A.—­The diameter of the crank pin in inches may be found by multiplying 0.02836 times the square root of the pressure on the piston in lbs. per square inch, by the diameter of the cylinder in inches.  The length of the pin is usually about 9/8th times its diameter, and the strain if all thrown upon the end of the pin will be equal to the elastic force; but in ordinary working, the strain will only be equal to 1/3d of the elastic force.

365. Q.—­What are the dimensions of the cross head?

A.—­If the length of the cross head be taken at 1.4 times the diameter of the cylinder, the dimensions of the cross head will be as follows:—­the exterior diameter of the eye in the cross head for the reception of the piston rod, will be equal to the diameter of the hole, plus 0.02827 times the cube root of the pressure on the piston in lbs. per square inch, multiplied by the diameter of the cylinder in inches; and the depth of the eye will be 0.0979 times the cube root of the pressure on the piston in lbs. per square inch, multiplied by the diameter of the cylinder in inches.  The diameter of each cross head journal will be 0.01716 times the square root of the pressure on the piston in lbs. per square inch, multiplied by the diameter of the cylinder in inches—­the length of the journal being 9/8ths its diameter.  The thickness of the web at centre will be 0.0245 times the cube root of the pressure on the piston in lbs. per square inch, multiplied by the diameter of the cylinder in inches; and the depth of web at centre will be 0.09178 times the cube root of the pressure on the piston in lbs. per square inch, multiplied by the diameter of the cylinder in inches.  The thickness of the web at journal will be 0.0122 times the square root of the pressure on the piston in lbs. per square inch, multiplied by the diameter of the cylinder in inches; and the depth of the web at journal will be 0.0203 times the square root of the pressure upon the piston in lbs. per square inch, multiplied by the diameter of the cylinder in inches.  In these rules for the cross head, the strain upon the web is 1/2.225 times the elastic force; the strain upon the journal in ordinary working is 1/2.33 times the elastic force; and if the outer ends of the journals are the only bearing points, the strain is 1/1.165 times the elastic force, which is very little in excess of the elastic force.