364 Mr. F. Y. Eclgeworth on the 
Is the shoemaker who makes a rather greater proportion of 
exact fits (who has a smaller probable error), but when he does 
make a misfit makes a terribly painful one, necessarily the 
most advantageous ? To quote Horace* again, the slave who, 
in spite of his many accomplishments, " semel latuit " (" once 
and but once I caught him in a lie," as Pope turns it), may 
have had, so to speak, a less "probable error," and yet may 
have been less " advantageous " to his master than one who 
had a greater number of less serious faults. The man who 
seldom tells a lie, but when he does " lies like a man," may do 
more harm than the habitual dealer in white lies. I am 
aware that there is something paradoxical in the preceding 
illustrations ; but I submit that it would be affectation in a 
mathematical writer not occasionally to glance at the real 
objects to which his ideal conceptions are applied, and that 
the disadvantages just instanced are quite homogeneous with, 
only more familiar than, the disadvantage due to the employ- 
ment in the arts of erroneous measurement (e. g. the disad- 
vantage of astronomical mismeasurement), the disadvantage 
which, according to Laplace and Gauss, it is the object of the 
calculus to minimize. 
The following is a more dignified example. Here are two 
instruments of observation, the errors incurred by which are 
ranged respectively under a probability-curve with modulus 
1 c 
unity, and under the facility-curve y= 5 s. where c is 
Ji ' J IT C~ + X 2 ' 
small. "Which of these instruments is to be preferred ? Ac- 
cording to Mr. Glaisher's test, unquestionably the latter. But, 
according to our view, it may well happen that the disadvan- 
tage in the long run is in the former case finite, in the latter 
case infinite: for example, if the disadvantage dependent upon 
a particular error may be expressed as any power (not less 
than the first), or sum of powers, of the extent of error. 
Nor, again, does the principle of greatest probability as 
compared with the principle of greatest utility give a con- 
sonant answer in the following case : — Given the law of 
error of a certain instrument, is it better to make a practice 
of confining ourselves to a single observation, or of proceeding 
to an average ? Upon Mr. Glaisher's view, if the average 
facility- curve is such as to have its maximum value (its head, 
so to speak) above the primary curve, the average must be 
preferable to the simple observation. This also follows from 
our first principle (by the theory of p. 363) iclien there is only 
one intersection behceen the primary and average semi-curves ; 
but not quite generally. Suppose that there are three inter- 
* Ep. II. 2. 
