## FANDOM

44,121 Pages

14 October 2011
Air rune 15 December 2007 11 6 Unchanged
Mind rune 10 3
Water rune 15 6
Earth rune 11 13
Fire rune 10 4
Body rune 9 5
Cosmic rune 140 107
Chaos rune 102 38
Nature rune 258 100
Law rune 304 158
Death rune 299 181
Astral rune 132 81
Blood rune 336 211
Soul rune 335 556

Calculations

From the old divisor obtained from the templates:

${div}_{\text{old}} = 14.0000$

We need to calculate a new divisor:

${div}_{\text{new}} = {div}_{\text{old}} \times \frac{\sum \left ( \frac{p}{q} \right )_{\text{new}}}{\sum \left ( \frac{p}{q} \right )_{\text{old}}}$

To calculate the new divisor, we need to find:

\begin{align} \sum \left ( \frac{p}{q} \right )_{\text{old}} & = \text{sum of ratios prior to change} \\ & = \frac{6}{11} + \frac{3}{10} + \frac{6}{15} + \dots + \frac{556}{335} \\ & = 8.93366198 \text{ (up to 8 d.p.)} \end{align}

And also:

\begin{align} \sum \left ( \frac{p}{q} \right )_{\text{new}} & = \text{sum of ratios prior to change} - \text{sum of removed ratios} + \text{sum of added ratios} \\ & = \sum \left ( \frac{p}{q} \right )_{\text{old}} - \text{sum of removed ratios} + \text{number of added items} \\ & = 8.93366198 - 0 + 1 \\ & = 9.933661982 \text{ (up to 8 d.p.)} \end{align}

Thus, the new divisor is:

\begin{align} {div}_{\text{new}} & = {div}_{\text{old}} \times \frac{\sum \left ( \frac{p}{q} \right )_{\text{new}}}{\sum \left ( \frac{p}{q} \right )_{\text{old}}} \\ & = 14.0000 \times \frac{9.93366198}{8.93366198} \\ & = 15.5671 \text{ (4 d.p.)} \end{align}
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