whence k = Σ R₁ F₁
——— .
Σ R₁²

The calculation of k becomes simplified when (as is generally the case in the tables) the loads R₁, R₂, &c., Rₘ are of the form,

N, 2N, 3N &c., m N.

In this case,

Σ R₁ F₁ = N (F₁ + 2F₂ + 3F₃ + &c. + mFₘ).

Σ R₁² = N² (1² + 2² + &c. + m²)

m(m + 1) (2m +1)
= N² ———————
6
(F₁ + 2F₂ + &c. + mFₘ)
k = 6 ————————— .
Nm(m + 1) (2m + 1).

In the case of [Table III].

m = 8, N = 14,