Example $3\mathrm{.}6$: A soil sample with a grain specific gravity of $2\mathrm{.}67$ was filled in a $1000$ ml con$-$

tainer in the loosest possible state and the dry weight of the sample was found to be $14\mathrm{.}75$ N $.$ It

was then filled at the densest state obtainable and the weight was found to be $17\mathrm{.}70$ N $.$ The

void ratio of the soil in the natural state was $0\mathrm{.}63.$ Determine the density index in the natural

state.