304 REMARKS ON TRAVELS 
ted should be on one side rather than another^ they mu- 
tually destroy each other^ and the more so^ the more the 
observations are multiplied. There is even a rule vrhich 
teaches us how much the sum found differs from the truth ; 
its discovery belongs to the learned geometrician, who is 
at present the organ of the French Institute for mathema- 
tical science. Knowing the error which may have oc- 
curred in an observation, it must be multiplied by the 
square root of the total number of observations. Thus, 
instead of growing with this number the total possible er- 
ror decreases proportionably. For example, for four ob- 
servations it would be represented by two, and for a hun- 
dred observations, by ten only. The proportion of 
total errors is therefore as ~° whereas the proportion of the 
number of observations is as ' f ^ : thus the error is but 
the fifth part of what it would be proportionally in four 
observations.* Hence it follows that the more obser- 
vations are multiplied the more any imperfection in the 
processes by which they have been made will be cor- 
rected. 
Are we not authorised to apply this principle to the 
length of M. Caiilie's stages, since the number of the 
lines of route is not less than six hundred and thirty three ? 
* I have formerly given a rather remarkable example of an analo- 
gous application, in the height of the great pyramid of Memphis, mea- 
sured by the assistance of mathematical instruments, and afterwards by 
the addition of the partial measures of the degrees, worked by imper- 
fect processes. The results differ very little, but the number of the 
partial measures was 203. 
