348 Prof. Potter on the Laws of the Expansion of 



following a law of uniform expansion, not being nearly repre- 

 sented by the formula V = V . e at \ I remembered my investiga- 

 tions in photometry, and resolved to apply a hyperbolic formula 

 to M. Drion's results. I have found that the volumes at dif- 

 ferent temperatures are as nearly represented by a hyperbolic 

 function of the temperature as can be expected, since the volumes 

 are the apparent ones shown by an instrument in the form of a 

 thermometer, and uncorrected for the amount of vapour in the 

 stem and the compressibility of the liquid under its pressure, 

 from want of the requisite 

 data. 



Let x, y in the an- 

 nexed figure be the rectan- 

 gular axes of coordinates, 

 and A P B an arc of a rect- 

 angular hyperbola. Then 

 for any point P, putting 

 PM = y, and OM=«, we 

 have the equation of the — — 

 curve in the form 



M. 



(y-a)(b-x)=c*, 



and of the five quantities 

 «, by c 2 , x, y we must have 

 the constants a, b, c 2 given 

 in order that the curve may be known. 



Now in the expansion of hydrochloric ether, if M = x repre- 

 sents the temperature, and PM=y the corresponding volume 

 of the liquid, then the three quantities a, b, c 2 can be calculated 

 from three sets of corresponding volumes and temperatures. 

 Having found the values of the constants in this manner, the 

 value of y for any other given value of x can be calculated by the 

 equation of the curve : 



ji 

 the volume =y=a~\- 



b—x 



By taking the first relation in the Table below, or that the 

 volume is taken unity at the freezing temperature of 0° C, always 

 for one of our three equations, and one of the others near the 

 middle, with the remaining one near the extreme of the series of 

 observations, the values of a, b, c 2 were found ; and then the for- 

 mula being applied to the remaining observed temperatures, and 

 the volumes calculated, they were found to show only small dif- 

 ferences from the observed results in every part of the series. 

 By varying the two latter equations near the middle and end of 

 the series, somewhat different values of a, b, and c 2 were found ; 



