208 
PRESTON. 
a thorough knowledge of the variations of latitude, the aber¬ 
ration of light, and the mean density of the earth. 
Congress has recognized this, and money has been appro¬ 
priated for the purpose. An observer was sent to Honolulu, 
and there, cooperating with astronomers in San Francisco, 
Washington, and Berlin, the change of latitude was studied 
during an entire year. The Honolulu and San Francisco 
results were discussed by the formation and solution of over 
9,000 conditional equations, nearly 7,000 of which appeared 
in one group and directly determined a single unknown 
quantity—the aberration constant. 
One might naturally inquire, What has the density of the 
earth to do with the measurement of angles on its surface ? 
The connection between them is best shown by an example : 
In a mountainous region a line was measured whose length 
did not agree with the known difference of latitude between 
the extreme points. To explain this discrepancy it was 
necessary to assume that the plumb-line was drawn out of 
its normal position, or that there was a disturbance in virtue 
of which the observed astronomical latitudes were not the 
true ones. The force of gravity was measured on the inter¬ 
vening mountain, which showed a density for the under¬ 
lying matter just sufficient to account for the attraction of 
the plumb-bob in obedience to the laws of gravitation. This 
interesting piece of work was done in the Hawaiian islands, 
where it was discovered that the pendulum on being carried 
to the summit of the mountain lost 28 oscillations per day 
instead of 41, as required by the law of the inverse square of 
the distance; The acceleration of 13 oscillations per day 
indicates a density of the mountain sufficient to deflect the 
vertical at its base by nearly half a minute of arc, which was 
precisely the observed discrepancy. 
The Transcontinental Arc. 
On the 3d of March, 1871, Congress made an appropriation 
“ for extending the triangulation of the Coast Survey so as to 
form a geodetic connection between the Atlantic and Pacific 
coasts of the United States.” 
