168 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1914. 
On representations from Count Cassini de Thuri to the Royal 
Society of London of the advantages that would be derived from the 
extension of the French triangle chain into England, the British Ord- 
*nance Survey was begun in 1784, and by 1851 the whole of the British 
Isles was covered with a network of triangles. This triangulation, 
however, as in the cases of all modern surveys, was designed to serve 
the double purpose of arc measurement and also as the basis of an 
accurate topographic survey. 
The year 1791 saw the inception of the grandest project ever devised 
for the establishment of a standard of length. Certain prominent 
members of the Academy of Sciences, among whom were Laplace and 
Lagrange, proposed to the Constituent Assembly of France—and 
received their sanction—that the ten-millionth part of the earth’s 
meridian quadrant be adopted as the national standard of length, to 
be called the meter. It was further proposed that this length be 
determined by the measurement of a meridian are extending from 
Dunkirk to Barcelona, and comprising 9° 40’ of latitude. This was 
accordingly carried out, the work being intrusted to Legendre and 
Mechain, and the length of the arc was found to be 551,584.7 toises, 
and its amplitude 9° 40’ 25’’. 
The commission appointed to revise their calculations and to deter- 
mine the length of the meridian quadrant combined this new French 
arc with the Peruvian arc, and thus found for the length of the 
meridian quadrant 5,130,766 toises, which gave as the length of the 
meter 0.5130766 in parts of the toise of Peru. 
It would be impossible even to notice briefly all the arc measure- 
ments that were now made in different countries, each contributing 
its quota to the growing mass of data for determining the earth’s 
figure. It is sufficient to state that in 1799 Laplace made a deter- 
mination of the elements of the spheroid based upon a discussion of 
nine meridian arcs measured in Lapland, Holland, France, Austria, 
Italy, Pennsylvania, Peru, and at the Cape of Good Hope. In this 
discussion Laplace made use of the expression 
d=A+B sin’ 
which gives the length of a degree of the meridian in a given latitude, 
A and B being functions of the semiaxes. As only two such equa- 
tions are necessary in order to determine the two unknowns, some 
principle had to be assumed in order to obtain the best values from 
all the measurements. Laplace adopted the principle that the un- 
knowns should be determined so as to fulfill the conditions that when 
substituted in the observation equations they should make the alge- 
braic sum of the errors in d equal to zero, and their sum, when all 
are taken positively, a minimum. This gave the expression 
d=56,753+ 613.1 sin’ 
