To determine the most appropriate tool for measuring the mass of a small feather, let's consider each option provided:
1. Pan balance: This tool is used to measure mass, typically by comparing the mass of an object with known masses on a balancing plate. While it can measure mass, it may not provide the precision required for the light weight of a small feather.
2. Meter stick: A meter stick is intended for measuring length or distance, not mass. Thus, it is not suitable for this purpose.
3. Graduated cylinder: This tool is used for measuring the volume of liquids. Since we're interested in measuring mass, a graduated cylinder would not be appropriate.
4. Digital scale: A digital scale is specifically designed to measure mass accurately, often with high precision. This makes it very suitable for measuring the small mass of a feather.
Considering these points, the most appropriate tool for measuring the mass of a small feather is the digital scale. Therefore, the correct answer is:
Digital scale