106 Mr. J. H. Alexander on the Tension of Vapour of Water, 



a deviation between the formula and the experiment but little 

 more than the admitted error of the thermometric readings. 

 The mean error of observation from this last source was found 

 just now to be +0°'28 F., and the mean error of the formula 

 then may be either 0°'08 or 0^"64 of Fahrenheit. These 

 quantities equally satisfy the equation, and the probabilities in 

 favour of each are even. 



It is observable that errors in this series come out with a 

 different sign from those of M. Regnault, though the errors 

 of observation in the two experimental series are nearly iden- 

 tical, as might be expected in advance from the great skill and 

 probably equal tact of the two observers. Such a difference 

 of sign is favourable to the character of the formula, which 

 will be seen by combining the two results, as under: — 



The nearness of these limits, and the smallness of the num- 

 ber inclosed by them, warrant, I think, a sole and entire reli- 

 ance upon the formula in the present state of experimental 

 knowledge on the subject. I do not introduce into combina- 

 tion any of the other and earlier series of observations; be- 

 cause, from the way in which they have been reported by their 

 respective authors, they do not admit the application of the 

 same methods of comparison ; and because it may justly be 

 supposed that the apparatus, intellectual and mechanical, re- 

 sorted to in 1829 and since, is paramount in accuracy to what 

 had been at disposal in preceding researches. 



I shall only, therefore, in further illustration of the present 

 formula, compare its results with those of expressions that 

 have been proposed by other mathematicians; only extending, 

 in point of fact, for this purpose, a similar comparison which 

 MM. Dulong and Arago have already instituted ; and using, 

 except for the last column, quantities from the calculation of 

 these philosophers. Their table is founded upon the same 

 eleven observations of their own, just now quoted ; and they 

 have given for each instance the individual deviations of the 

 several formulae from the result of experiment. Not to em- 

 ploy so much room, I have thought it equally satisfactory to 

 give the general results and inferences, as under. The devi- 



