If we measure a pound of feathers and a pound of lead and drop them from a second story, one object will float to the ground and the other will drop so fast it could injure passers-by. The difference is due to a property of matter called “density.” Water displacement is one of the ways that we can measure density, particularly density of irregularly shaped objects. But feathers float and require a special technique to measure displacement.
Fill the graduated cylinder partially with water to a level where you can submerge the object and drop the sinker weight into the water. If you don't have a graduated cylinder to fit your object, put a cylinder in a basin, fill it to the top with water and measure the overflow into the basin. Your answer will be less accurate because of the number of times the water has been moved. Note the amount of displacement in milliliters (ml) caused by the sinker and string.
Measure the mass of your object (say a cork) on a balance scale in grams (g). Be sure the object is dry when it is measured. Record its weight. Attach the sinker with the string to the object. If you use a staple or pin, be sure to include that when you measure the displacement of the sinker in step one.
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Drop the sinker with the attached floating object into the cylinder. If the entire object does not sink, you may need to use a heavier sinker. If so, be sure to measure the displacement of the new sinker and line so the whole object will sink below the surface. When the entire object is submerged, note the volume of the total displacement in milliliters, measuring the volume from the center of the water column, not the edges where surface tension and capillary action affect the reading.
Subtract the volume of the water and sinker assembly from the volume of the water, sinker assembly and submerged object. The result will be the volume of the object alone. This volume in milliliters is equivalent to square centimeters (cm).
Divide the weight (M) of the object in grams by its volume (V) in square centimeters. The result will be its density (p) expressed in grams per square centimeter. Objects that float all have densities of less than one gram per square centimeter, the density of the water in which they float.
TL;DR (Too Long; Didn't Read)
The material of feathers is not only less dense than lead, they contain numerous hollow spaces that contribute to the aerodynamic stability of a bird's wing.
Density readings will be approximate--variations in temperature and atmospheric pressure will have slight effects on the density of the water used to compute the density for your object.