| 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,