In determining the stadia interval factor $(K)$ of a transit, a stadia rod was held vertically at several points along measured distances from the instrument, and the corresponding stadia hair readings were observed.

The distance and the observed readings were recorded as follows:

$\backslash$table$[[$Point$,\backslash$table$[[$Distance from$],[$transit to rod$]],$Stadia hair readings$],[$Upper $(m),$Lower$($m$)],[a,30,0\mathrm{.}96,0\mathrm{.}66],[b,45,1\mathrm{.}10,0\mathrm{.}64],[c,60,1\mathrm{.}21,0\mathrm{.}60],[d,75,1\mathrm{.}35,0\mathrm{.}58],[e,90,1\mathrm{.}47,0\mathrm{.}56],[f,105,1\mathrm{.}57,0\mathrm{.}53],[g,120,1\mathrm{.}72,0\mathrm{.}50]]$

Determine the stadia interval factor of the instrument. Assume that the stadia constant $C$ is zero.