MATHEMATICAL SECTION. 155 
In practical problems the antecedent probability of blunders and 
other uninstructive errors is never known, and is only matter of 
exceedingly vague conjecture. Perhaps if a very large number of 
observations were examined, and the proportion of evidently unin- 
structive errors ascertained, a somewhat intelligent estimate might 
be made of the proportion of those that exist but are not evident; 
and data of some little value might be gathered toward a scientific 
method of weighting. But Ihave no faith that the result would 
be any where near worth the labor. At present, the best that a 
computer can do is to reject entirely, or retain entirely, or assign 
a simple weight, such as 3, 3, or #, in sheer desperation, and with 
the feeling that his judgment is nearly or quite worthless. It would 
be utter folly to assign weights upon a centesimal scale; and it 
would also be utter folly to conjecture an antecedent probability 
and proceed according to the method just set forth. 
It is well known that the method of least squares gives very un- 
trustworthy information in regard to the antecedent probability of 
large instructive errors. In regard to the other antecedent proba- 
bility required for an intelligent solution of the problem, it gives 
no information whatever. So far as I can understand Prof. 
Peirce’s method of arriving at a criterion, he takes two probabili- 
ties, both functions of probabilities of instructive error, and balances 
them against each other. This procedure reminds me of what 
sometimes haj.pens in war, when two detachments of the same 
army meet in the dark and fire into each other, each supposing the 
other to belong to the common enemy. Prof. Peirce also seems to 
me to violate the fundamental principle of the science of probabili- 
ties, that probabilities must be independent in order that their 
product shall equal concurrent probability. 
If a computer resorts to the criterion when he feels that his own 
judgment is worthless, and only then, the criterion is harmless ; 
since it is of no importance whether a decision is made by a worth. 
less judgment or a worthless criterion. 
In the discussion that followed, Mr. A. HAuu gave a brief account 
of the literature of the criteria which have been proposed for the 
rejection of doubtful observations. In addition to the criterion 
proposed by Prof. Peirce,,which had been discussed by Mr. Doolit- 
tle, that of Mr. E. J. Stone was mentioned; and also the proofs 
of a criterion given by Chauvenet and Watson. The advocacy of 
of Peirce’s criterion by Gould, Winlock, Bache, Coffin, and Schott 
