Mr. J, H. Alexander on the Tension of Vapour of Water. 99 



remained to complete this memoir, in showing the probable 

 errors of the formula as compared with the principal experi- 

 ments, and with the probable errors affecting too those differ- 

 ent series of experiments themselves. Such a discussion is 

 the object of the present paper. 



It was already said in the preceding part, that the most 

 proper mode of expressing these errors is by the linear scale 

 of temperature; which both in theory is the most important, 

 and in practice is the most accessible and usual. In this last 

 aspect, it is on this scale, too, where errors of observation are 

 the most easy to be made, and likely to occur. With this 

 view the formula need be repeated here only in its converse 

 form {i. e. for ascertaining temperatures from given pressures), 

 as under: — 



^^ Fahr. = 1 80 -1^^- 1 05°- 1 3 ; 



p being in inches of mercury ; and 



^°Fahr. = 317-13 Vp'-105°'13; 



y being in atmospheres at 32°. 



As this will have to be frequently applied for interpolation 

 throughout the following discussion, it may be as well to re- 

 mark here, once for all, in justification of such application, 

 that there need be no apprehension of its affecting the results; 

 for it is easy to see, by inspecting a few instances taken at ran- 

 dom from the table, that the rational deviation of the formula 

 {i. e. the difference between calculated and observed pressures) 

 is, for small differences of temperature, either null, or so re- 

 mote a fraction as to be inappreciable in the calculation. 



In applying this formula, I shall take up the principal series 

 of experiments separately, beginning with the most recent, 

 and shall then make assemblage of the mean results. 



1. Experime7its of M. Regnault, — To deduce the absolute 

 mean error of the numerous quantities of this observer, it 

 would be obviously requisite to take up each experiment ; a 

 labour of which I am by no means ambitious, and which would 

 be disproportionate at once to what is admissible in the other 

 series presently to be noticed, and to the present aim. I shall, 

 therefore, in all only make use of short general methods, which, 

 without laying claim to the accuracy of geometrical refine- 

 ments, will yet be recognized as having foundation in the 

 theory of mathematical probabilities ; and will, by their po- 

 pular form, recommend themselves the more readily to the 

 convictions of those who are chiefly conversant with steam in 



H2 



