How far, and in what direction, should a cellist move her finger to adjust a string's tone from an out$-$of$-$tune $455$ Hz to an in$-$tune $440$ Hz$?$ The string is $68\mathrm{.}0$ cm long, and the finger is $18\mathrm{.}1$ cm from the nut for the $455-$Hz tone. $($Assume the tone comes from the portion of the string between the cellist's finger and the end opposite the nut. Assume the string vibrates in the fundamental mode. Take the direction towards the nut to be positive. Indicate the direction with the sign of your answer.$)$