The Plan of the Earth and its Causes. — Gregory. 137 
hemisphere. If that be the case, then the peg-top elongation 
is all the greater. 
Morevoer, there is evidence to show that the earth's figure is 
still more irregular than that of a peg-top.'^ Sir John Her- 
schel, although taking the astronomical side in the controversy,, 
aptly stated the facts in the statement that " the earth is earth- 
shaped." Listing's name of geoid, which expresses this view, 
has now supplanted the old oblate spheroid from everything 
except the text-books. That there are local deformations in 
the earth's shape is demonstrated by the differences between 
the astronomical and trigonometrical determination of posi- 
tions. Places have two different longitudes, the astronomical 
longitude obtained by astronomical observations, and geodetic 
longitudes determined by terrestrial measurements ; the differ- 
ences are often considerable. It was calculated, e.g., that the 
trigonometrical and astronomical determinations of the sta- 
tions used in the delimination of the Canadian and United States 
frontier should have agreed within 40 feet, or 0.4 of a second 
of arc ; but the average error was more than five times as great, 
and ran up to eighteen times as much as it should have been. 
Astronomical determinations, moreover, are often not only 
inconsistent with geographical measurements, but they are 
often inconsistent with themselves. For example, one of the 
most refined estimations of longitude that have yet been at- 
tempted, is the series undertaken by the "K. K. topographische- 
militar Institut" of Vienna. To ensure accuracy during these 
observations, the most elaborate precautions were taken. Cor- 
rections were even made for the effect of the doses of quinine 
which the astronomers took when working in malarial cli- 
mates. In one of the series of observations, the difference in 
longitude between \ ienna and Milan was determined first di- 
rectly, and then l)v determining the difference between Vienna 
and Brescia and that between Brescia and Milan. But in spite 
of all the care, the results did not tally. The sum of the two 
differences was not the same as the single difference. The 
whole, in fact, in this case was less than the sum of its parts. 
To astronomers it ma}' seem an unnecessary waste of time 
to devote so much to proving these deformations from the 
"spheroid of reference." liut as the idea is less familiar to 
* As Prof. Darwin suggests, potato-shaped would be a more correct simile. 
