THE TRANSCONTINENTAL ARC. 
217 
pendulums for the determination of the absolute force of 
gravity in each particular locality. Later, when it was 
found to be much more difficult to measure its length than 
to determine the time of oscillation, observers went back to 
relative work and adopted the invariable instrument. Then 
it suddenly appeared that all necessary accuracy could be 
attained and results produced more rapidly by making the 
pendulum one-fourth as long, and therefore oscillating in 
one-half the time. That is where we are at present, and the 
greater part of the measurements of the force of gravity 
throughout the world today are made with half-second pen¬ 
dulums. The two principal types of apparatus are those em¬ 
ployed by the Austrians and the Americans. Either form 
will give an accuracy in the period of about double that 
formerly obtained. A comparatively short experiment will 
now furnish us with the time of oscillation within one-mil¬ 
lionth of a second. 
With regard to the treatment of the results, there is still 
some difference of opinion. A French observer made pend¬ 
ulum experiments in Peru about 150 years ago. Although 
his instrument was but a piece of lead suspended by a string 
cut from a native plant, the result obtained has been verified 
by modern observers in many parts of the world. Having 
compared the times of oscillation at the sea-level and at the 
summit of the Andes, he found that the decrease of the force 
of gravity was not as much as he expected from Newton’s 
law of the inverse square of the distance. The discrepancy 
was attributed to the downward attraction of the mountain 
mass between the summit and the sea. An estimate was 
made of the density of the earth’s crust and a mathematical 
formula was evolved for the reduction of gravity observa¬ 
tions to the sea-level. This is the first application of such a 
correction. Now we come to the point mentioned a moment 
ago, viz., that the Peruvian work has been confirmed by later 
observations. Correcting the result for the supposed attrac¬ 
tion of the mountain, it was found that the Andes under this 
supposition were not much heavier than water. Strange as 
