FORM AND CONSTITUTION OF EARTH-—STEWART. 169 
for finding the length of a degree in any given latitude. On applying 
this expression to the Lapland arc, however, it was found to give a 
value 138 toises shorter than that found by observation, from which 
Laplace concluded that the earth deviates considerably from the 
spheroidal form. It must be mentioned, on the other hand, that in 
1801 an expedition was sent from Stockholm in charge of Svanberg 
with instructions to measure the Lapland are, with the result that 
he found for the length of 1° a value about 200 toises less than that 
found by Maupertuis, thus conforming more closely to the value 
given by Laplace’s empirical formula. 
During the nineteenth century geodetic work was carried on vig- 
orously by every civilized nation, and great improvements were intro- 
duced in instruments and methods. The result of this activity is that 
we now have the following arcs available for investigating the earth’s 
figure: The British-French arc, extending from the Shetland Isles 
through France into Africa, and covering 27° 01’ of latitude; the 
Russian are, extending from the Danube to the North Sea and having 
an amplitude of 25° 20’; the arc of the parallel in latitude 52°, extend- 
ing from the west coast of Ireland to the Ural Mountains and embrac- 
ing 68° 55’ of longitude; the are lately measured in Spitzbergen 
between latitudes 76° 38’ and 80° 50’ N., which is important on ac- 
count of its high northern latitude; the Indian ares, including 24 
meridian arcs and 7 arcs of parallels of latitude; the South African 
arc; the Peruvian arc, lately remeasured; the American oblique are 
following the Atlantic coast for a distance of 1,623 miles; the western 
oblique are, extending along the Pacific coast; the are of the parallel 
of latitude 39° N., extending from the Atlantic to the Pacific; the 
ninety-eighth meridian arc, now well under way and to which Canada 
and Mexico have been invited to contribute their shares and which 
when complete will extend over 50° of latitude. 
A proposal made by Sir David Gill should be here mentioned. 
When director of the Royal Observatory at Cape Town he instituted 
the project of extending the South African triangulation through 
Natal and then on through the whole extent of the African Continent, 
following the meridian of 30° of east longitude, to Cairo, and thence 
on to connect with the Russian are on the Black Sea. This are will 
have a total amplitude of 105°. 
The application of the electric telegraph to longitude determination 
has given measurements of ares of parallels of latitude an importance 
in these investigations fully equal to that of meridian arc measure- 
ments. 
As additional data became available investigations were made from 
time to time to determine the spheroid that would best represent the 
measured arcs. The most important of these were those made by 
Bessel in 1841; Col. A. R. Clarke, of the British Ordnance Survey, in 
