100 Prof. Potter on Mr. Alexander's formula 



observers as closely as they accord with each other, to be con- 

 clusive. 



When we consider the formula, we can see that the nature of 

 the experiments must be such that extreme accuracy is unattain- 

 able with even the most improved apparatus. When p is the 

 elastic force of the vapour expressed in the pressure of a column 

 of inches of mercury, t the temperature expressed in Fahrenheit's 



/ t 990 \ 6 



degrees, then Mr. Alexander's formula is p = (yon"*" 1C95/' 



The binomial being to the sixth power, a small error in the value 

 of t, either in the graduation of the thermometers or in the ob- 

 servations, produces a considerable change in the value of.jo; 

 and if both errors existed at. the same time and in the same di- 

 rection, the error in the value of p might become large. We 

 have no need to be surprised that even the results of M. Reg- 

 nault require this consideration to be kept in mind, and it is the 

 general accordance through long ranges of temperature that we 

 must look for, rather than great accuracy at all points, which 

 the subject is not capable of giving. 



Having long ago compared Mr. Alexander's formula with the 

 results for the elastic force of several vapours given at page 298 

 of Dalton's 'New System of Chemical Philosophy,' part 1st of 

 vol. ii., and found the accordance satisfactory, I have lately un- 

 dertaken the comparison with M. Regnault's results in the 

 second volume of his Relation des Experiences, &c, pp. 374 and 

 forwards. The result of these investigations is contained in the 

 following pages. 



To adapt Mr. Alexander's formula for the elastic force of steam 

 to that of the vapours of other liquids, let p be the pressure, let 

 a and b be constants, and t the temperature, then we have 



p=(a + bt) 6 . 



Now M. Regnault's results give p in columns of millimetres 

 of mercury, and t in Centigrade degrees ; so that I shall give 

 the procedure and results in these terms at first, and afterwards 

 show the formulae for p in inches of mercury, and t in Fahren- 

 heit's degrees. 



For vapour of alcohol, in the formula p = (a + bt) 6 , putting 

 t° C. =0, at the freezing-point of water M. Regnault found 



p — 12*70 millims. =a 6 ; 



.\ a= 1-527451. 



Again, at 150° C. he found 



p= 7318-40 millims. = (1-527451 + 150&) 6 ; 



.\ £ = -0191920. 



