record the beaker with the sixty drops weight. Then weigh after the second sixty drops is added.
density=volume/mass= sixty drops/changeinmass
that will give you the density in drops/gram
if you want grams per drop, then do the reciprocal.
Now, for drops per ml. You know the density of water, 1g/ml. So the change in weight you recorded for the second sixty drops is = change in ml.
60/changeinml (same as change in grams).
#drops x (grams/drop) = grams.
You know # drops. You know grams. Calculate grams/drop and take the reciprocal.
Since mass = volume x density you can calculate the volume of the 120 drops.
Then if 120 drops = xx mL, how many drops per 1 mL.
You must remember that the number of drops in a mL will depend upon how the drop is added; i.e., it will be different from an eye dropper than it is from a teflon coated tip of a buret.
The OLD glass tipped buret I used years ago gave very close to 20 drops/mL. Through the years the tip was refined and it was about 25 drops/mL. With the teflon coated tips and smaller tips, it is about 30 drops/mL now.
I would add one caveat to Bob Pursley's response. Check the density of water at the temperature of the water being dispensed by drops. The density may not be significantly different from 1.00 g/mL but it won't hurt to check it and see if it makes a difference.