354 Expansion of Transparent Liquids by Increase of Temperature. 



For esseutial oil of turpentine (terebene), taking the tempera- 

 tures 0° C., 68°-86 C., and 149°-59 C, I find the values of a, b, 

 and c 2 as follows : — 



a = -1833844, 



b = 884-4142, 



c 2 = 722-2265, 



which give the results in the Table annexed. 



Temperature 

 by Centigrade 

 thermometer. 



Volumes of oil 



of turpentine 



observed, being 



1 at 0° C. 



Volumes 

 calculated by 

 the formula. 



Differences. 



0- 



1-0000000 



1-0000000 



•0000000 



21-81 



1-0204450 



1 0206474 



+ -0002024 



4376 



1-0425062 



1-0425088 



+ -0000026 



68-86 



1 0689505 



1-0689494 



- -0000011 



90-08 



1-0926244 



1-0926066 



-•0000178 



90-14 



1-0926861 



1-0926754 



-•0000107 



111-27 



1-1178598 



11175264 



- -0003334 



130-96 



1 1423470 



1-1419384 



- -0004086 



149-59 ' 



1-1662405 



11662404 



- -0000001 



157-28 



11767301 



1-1766349 



-•0000952 



The differences between the observed and calculated values are 

 small, commencing when largest with small numbers in the 

 fourth place of decimals; and we must conclude that oil of tur- 

 pertine is subject to the law of hyperbolic expansion. 



In the geometrical representation of our problem we have 

 employed the equation (y — a){b—x) — c i i and it must be homo- 

 geneous ; that is, y representing a volume of the liquid, a repre- 

 sents a volume also ; and x representing degrees of temperature, 

 b represents degrees of temperature also. The quantity c 2 con- 

 sequently represents a product of a volume and a temperature. 

 For convenience, putting c' for the volume, and c' f for the tem- 

 perature, and c 2 =c ; . c", we have 



c" 

 volume y— vol. «+ vol. c' x , 



* b—x 



In this expression it is evident that we may change the unit of 

 volume without altering the units or degrees of temperature, and 

 the converse, and the equation will remain homogeneous. As, 

 for instance, we might, with M. Pierre, take the volume of the 

 liquid at its boiling-point for the unit of volume, and leave the 

 degrees of temperature those of the Centigrade scale. 



On the other hand, we may leave the unit of volume that of 

 the liquid at the freezing-point of water, and change the unit of 

 temperature to that of the natural scale with the freezing-point 

 zero, and the interval from freezing to boiling of water unity 



