442 
negative errors would be equally probable. But there is 
another class of errors involved, belonging to the Tables of 
the elastic force of vapour at different temperatures. In 
fact, the value of m being expressed in terms off, and f 
being calculated from the observed value of ¢, by these 
Tables, it is obvious that the errors of the Tables will affect 
the result. In this point of view, however, there is a very 
important difference between the second series of experi- 
ments and the other two. The values of m, in the first and 
third series, are expressed in terms of the difference of two 
values of f ; so that any constant error, in the Tables which 
give the values of f, must wholly disappear in the result ; 
and any error nearly constant must, for the same reason, be 
nearly evanescent. The case is different, however, in the 
second series. Here m is expressed in terms of a single 
value of f; and the tabular error of that value has therefore 
its full effect. Now, that the errors of the Tables are 
of the kind alluded to,—i.e. nearly constant within certain 
moderate limits of temperature,—will be evident from the 
mode in which they are constructed. The value of f is 
in all cases calculated from an empirical formula, which 
(within the ordinary range of temperature) does not vary 
rapidly with moderate changes of ¢; the error in the value 
of f, therefore, (i. e. the difference between its value as cal- 
culated with the assumed and with the ¢rwe formula,) may, 
therefore, be regarded as nearly the same, for a moderate 
range of the variable on which it depends. 
It follows from this, that, in the second series, the true 
probable error is greater than that deduced from the obser- 
vations themselves, and is the resultant of that error and 
of the error of the Tables. If this latter error were known 
@ priori, the resultant error could be inferred; but as this 
is not the case, we have no means of knowing the weight 
due to the result of that series, and have, therefore, no rule 
to guide us in combining that result with the other two. 
