the geodesic Operations of the Meridian of France. 135 
sure of this base, and its value deduced from the Perpignan base, 
would not exceed one-third of a metre. This is nearly the dif- 
ference between the measure of the Perpignan hase and its value 
deduced from the base of Melun. It appears in the quoted Sup- 
plement, that the angles having been measured by means of a 
repeating circle, we may suppose the probability of an error x 
iu the observed sum of the three angles of every triangle, pro- 
portional to the exponential c_"*’, k being a constant quantity; 
whenee it follows that the probability of that error is 
dxf i. gs 
Ae 
a denoting the ratio of the circumference to the diameter. 
By multiplying it by x, taking the integral from a null to x 
infinite, and doubling this integral, we shall evidently have the 
mean error, by taking the negative errors positively. ‘This mean 
error being then denoted by 1, we shall haye 
1 
= 
We shall have the mean value of the square of these errors, by 
multiplying by 2 the preceding differential, and integrating it 
from «= — ©, to x infinite; calling then ¢ that value, we shall 
have 
>] 
ya} 
2, 
Hence we deduce c= — 
Thus § may be obtained by means of the errors, taken all plus, 
of the sum observed of the angles of every triangle. In the 107 
triangles of the meridian, this sum is by what precedes, 173,52; 
3,82 
173,82 : j 
we may consequently take for s, raeane which gives for 26. ¢, or 
for 6? 
f= 264 (<= 
2 fod 
aot \ 10% ) spore. 
This differs very little from the value 108,134 given by the 
sum of the squares of the errors of the observed sum of the an- 
gies of every one of the 107 triangles. This agreement is re- 
markable. 
By supposing the angle of intersection of the Perpignan base, 
with the meridian which passes through one of the extremities 
of this base, well determined ; we should have exactly the angle 
of intersection of the meridian with the last side of the chain of 
triangles which unite this base to the isle of Formentera, if the 
earth was a spheroid of revolution, and if the angles of the ot 
angles 
