Falling Body Measurements
The gravitational acceleration can be measured directly by dropping an object and measuring its time rate of change of speed (acceleration) as it falls. By tradition, this is the method we have commonly ascribed to Galileo Galilei. In this experiment, Galileo is supposed to have dropped objects of varying mass from the leaning tower of Pisa and found that the gravitational acceleration an object undergoes is independent of its mass. He is also said to have estimated the value of the gravitational acceleration in this experiment. While it is true that Galileo did make these observations, he didn't use a falling body experiment to do them. Rather, he used measurements based on pendulums.
It is easy to show that the distance a body falls is proportional to the time it has fallen squared. The proportionality constant is the gravitational acceleration, g. Therefore, by measuring distances and times as a body falls, it is possible to estimate the gravitational acceleration. To measure changes in the gravitational acceleration down to 1 part in 40 million using an instrument of reasonable size (say one that allows the object to drop 1 meter), we need to be able to measure changes in distance down to 1 part in 10 million and changes in time down to 1 part in 100 million!! As you can imagine, it is difficult to make measurements with this level of accuracy.
Although absolute gravimeters are more expensive than the traditional, relative gravimeters and require a longer station occupation time (1/2 day to 1 day per station), the increased precision offered by them and the fact that the looping strategies described later are not required to remove instrument drift or tidal variations may outweigh the extra expense in operating them. This is particularly true when survey designs require large station spacings or for experiments needing the continuous monitoring of the gravitational acceleration at a single location. As an example of this latter application, it is possible to observe as little as 3 mm of crustal uplift over time by monitoring the change in gravitational acceleration at a single location with one of these instruments.