442 



negative errors would be equally probable. But tbere 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 of/, and/ 

 being calculated from the observed value of t, 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 off ; 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/,- 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/ is 

 in all cases calculated from an empirical formula, which 

 (within the ordinary range of temperature) does not vary 

 rapidly with moderate changes of t ; the error in the value 

 of /, therefore, (i. e. the difference between its value as cal- 

 culated with the assumed and with the true 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 

 h 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. 



