Handbook of Railroad Construction; For the use of American engineers. / Containing the necessary rules, tables, and formulæ for the location, construction, equipment, and management of railroads, as built in the United States.

by George L. Vose

where a = area of rivet,

d = distance,

t = plate thickness.

also

2d′ + d = R × d
R′;

and

2d′ = R × d
R′ – d;

whence

d′ = [R × d
R′ – d]/2

and finally