Mr. J. H. Alexander on the Tension of Vapour of Water. 103 



This mean difference (say 0°'6i F.) is the error of the for- 

 mula as compared with the ob.servations above, which are 

 themselves the mean of more than twice as many experiments, 

 and which may be taken as representing impartially the whole 

 ranjre of M. Reffnault's results. In arriving at this mean 



o CD , . . 



difference, I have arranged the several instances into groups, 

 whose individual means furnish the definitive general (me. 

 This is proper, in view of the different methods of experiment 

 which the different relations of temperature in the respective 

 groups rendered necessary. The indiscriminate mean of all, 

 however (0°'657 F.), is not materially variant. It will be seen 

 that, up to the point of boiling water, the formula-temperatures 

 are generally /otU(?r than experiment; above that point, they 

 are in general higher. I believe that such a change of sign 

 accords with what might be anticipated, and in so far does 

 not diminish the reliability of the formula. 



The difference ( + 0°-61 F.) would be the absolute error of 

 the formula, were we to assume the experiments as perfectly 

 accurate. But they have been already siiown to be themselves 

 affected by an error of +0°-31 F. ; and the absolute error of 

 the formula, then, may be either 0°-30 or 0°-92 F., according 

 as the equation is made of the sum or the difference. Either 

 of these quantities may in the theory represent the true error; 

 and we have, therefore, in fine, the case of an even chance for, 

 accuracy with the formula or with the observation. . .; 



