134 Application of the Calculation of Probabilities to 
Formentera, including an arc of the meridian of about 466006 
metres, the probability of an error s is proportional to the expo- 
nential. 
— 9. ns? 
ce 92;48350,606" 
c is the number which has unity for its hyperbolic logarithm; 
m is the number of triangles employed; 4? is the sum of the 
squares of the observed errors in the sum of the three angles of 
every triangle; lastly, s is the error of the total arc, the base of 
Perpignan being reckoned unity. Here m is equal to 26. By 
taking the sexagesimal second for the unity of angle, we have 
; G7=='188,178, 
But the number of triangles employed being only 26, it is pre- 
ferable to determine by a greater number of triangles the con- 
stant §*, which depends on the unknown law of the errors of the 
partial observations. ‘To do this, use has been made of the 107 
triangles employed to measure the meridian from Dunkirk to 
Formentera. The whole of the errors of the observed sums of 
the three angles of every triangle is, by taking them all positively, 
173,82 : the sum of the squares of these errors is 445,217. By 
— we shall have for the value of 6? 
#= 108,134, 
This value differing but little from the preceding, ought to be 
employed in preference. It must be reduced into parts of the 
radius of the circle, by dividing it by the square of the number 
of sexagesimal seconds which this radius contains; then the 
preceding exponential becomes 
-— (689,797)*.$*5 
so that the base of Perpignan being taken for unity (689,797)? 
is what I name the weight of the result, or of the arc measured 
from the signal of Burgarach to Formentera. This base is 
11706™,40; hence it has been concluded that the following frae- 
tions, which approach unity very nearly, are the respective pro- 
babilities that the errors of the arc in question are comprehended 
within the limits +607, +50", +40". 
1743695, 32345, 1164 
1743696? 32346? 1165" 
No reasonable doubt therefore can be entertained respecting the 
exactitude of the measured arc. The limits between which it 
may be wagered one to one that the error falls, are +8™,0937. 
If a base of verification, equal to the Perpignan base, was mea- 
sured on the coast of Spain, and joined by two triangles to the 
chain of triangles of the meridian ; it is found by calculation, that 
one to one may be wagered that the difference between the mea- 
sure 
multiplying this sum by 
: 
: 
1 
: 
