156 PHILOSOPHICAL SOCIETY OF WASHINGTON. 
was noticed, and also its criticism by Airy, Sténe, and Glaisher, 
together with Glaisher’s approval of De Morgan’s method of 
treating observations. In conclusion, Mr. HAut said: 
The general result of what has been done in this matter appears 
to be as as follows: 
Every one can devise a criterion that suits himself, but it will not 
please other people. 
Now there seems to be a good reason underlying this. The 
attempt to establish an arbitrary and general criterion for the dis- 
cussion and rejection of observations is an attempt to eliminate 
from this work the knowledge and judgment of the investigator. 
Such an attempt ought to fail, and it certainly will fail at length, 
no matter by what personal influence it may be supported. It is 
true that no proof has been given of the principle of the arith- 
metical mean for a finite number of observations, such as the prac- 
tical cases that always come before us; but we assume this principle 
as leading to the most probable result. When we depart from this 
principle, it must be done, I think, for reasons that are peculiar to 
each case, and there can be no better guide than the judgment of 
the investigator. It may be said that if the criteria that have 
been proposed be carefully managed they will do little harm, since 
the result of the arithmetical mean will be altered very little; and 
in fact this is their chief recommendation. But by diminishing 
the value of the real probable error the criteria give to the observ- 
ations a fictitious accuracy and a weight they do not deserve. 
The paper was also discussed by Messrs. Hit, Exuiorr, Far- 
QUHAR, WoopWARD, and others, including Mr. JAmMEs Maryn, a 
visitor—all agreeing, on essential points, with Mr. Doolittle’s view. 
Mr. R. S. WoopwAkrp then discussed 
THE SPECIAL TREATMENT OF CERTAIN FORMS OF 
OBSERVATION-EQUATIONS. 
[ Abstract. ] 
In a set of observation-equations whose type is 
z+ (t—t,) y—n =v with weight p, 
in which ¢, is an arbitrary constant, the same for éach equation, 
and in which the residuals, v, are supposed to arise solely from 
errors in the observed quantities, n, it will be best to make 
pea 
2 
