figure of the earth. 569 
meters there were some errors in the reduction of the base, 
which exactly corrected the difference (Tome iii. p. 136). 
The semi-module, therefore, in the expression for the arc of 
the meridian, is exactly equal to the toise of Peru at the 
temperature of i6°|- centigrade. 
The standard metre at the temperature of o° centigrade 
= 443,296 lines of the toise of Peru at 1 6°^ centigrade 
(p. 139 ). 
The standard metre at the temperature of o° centigrade 
was found by Captain Kater (Philosophical Transactions 
1818) to be = 39,37079 inches of the English standard at 
the temperature of 62° Fahrenheit. 
Consequently the semi-module in the expression for the 
arc of the meridian is = 1,065766 fathoms measured by the 
English standard at the temperature of 62° Fahrenheit ; 
and since the English and Indian measures are estimated by 
this standard at the same temperature, no reduction is to be 
made for temperature. (The degree between Paris and 
Evaux is found thus to be 60822,5 fathoms ; Col. Lambton 
has stated it to be 60779 fathoms). The length of the French 
arc given below, in fathoms, is therefore found by merely 
multiplying the number of semi-modules by 1,065766. 
The English arc has the corrections which Captain Kater 
has given in the Phil. Trans, for 1821. 
The Swedish arc is taken from Svanberg's Exposition des 
Operations, &c. supposing their standard compared with the 
French standard at the temperature of o° centigrade. 
Thus the following table is formed. 
