Editing Gridiron pendulum (section)

===Five rod gridiron===
In the 5 rod gridiron, there is one high expansion rod on each side, of length <math>L_\text{2}</math>, flanked by two low expansion rods with lengths <math>L_\text{1}</math> and <math>L_\text{3}</math>, one from the pivot to support the bottom of <math>L_\text{2}</math>, the other goes from the top of <math>L_\text{2}</math> down to support the bob.<ref name="Matthys" />  So from equation (3) the condition for compensation is
:<math>{\alpha_\text{high} \over \alpha_\text{low}} = {L_\text{1} + L_\text{3} \over L_\text{2}}</math>
Since to fit in the frame the high expansion rod must be equal to or shorter than each of the low expansion rods  <math>L_\text{1} \ge L_\text{2}</math> and <math>L_\text{3} \ge L_\text{2}</math> the geometrical condition for construction of the gridiron is
:<math>L_\text{1} + L_\text{3} \ge 2L_\text{2}</math>
Therefore the 5 rod gridiron can only be made with metals whose expansion coefficients have a ratio greater than or equal to two<ref name="Matthys" /><ref name="Baker2005" />{{rp|p.251}}
:<math>{\alpha_\text{high} \over \alpha_\text{low}} = {L_\text{1} + L_\text{3} \over L_\text{2}} \ge 2</math>
[[Zinc]] has a CTE of <math>\alpha</math> = 26.2 ppm per °C, versus the steel value of 11.5, so the ratio of <math>\alpha_\text{high}/\alpha_\text{low}</math> = 2.28.  Thus the zinc/steel combination can be used in 5 rod pendulums.<br/>  
The compensation condition for a zinc/steel gridiron is
:<math>{L_\text{1} + L_\text{3} \over L_\text{2}} = 2.28</math>