EXPANSION OF LIQUIDS. 



33 



Regnault made, in all, about 130 observations in the range of 

 temperature from 25 0. to 350 C., and from these he constructed a 

 table of expansions by a "graphic" method, i.e. by representing his 

 results on a volume-temperature diagram. The principle he adopted is 

 as follows : Taking two lines at right angles, and marking along one 

 temperatures and along the other the volumes assumed by the mass 

 which has at the volume 1000, each observation will be represented 

 by a point on the diagram. If the observations were perfectly free 

 from error, we might expect that all these points would lie on a regular 

 curve or a straight line, the true curve which we seek to determine. 

 But through imperfections in the measurements of length and tempera- 

 ture, the points will probably lie sometimes above, sometimes below the 

 true curve. 



Let us suppose that the observations are indicated by the crosses in 

 Fig. 24. Then a curve is drawn so as to pass as nearly as possible midway 

 through the points, i.e. 



so as to make the sum , J-/0/6 



of the heights above 

 the curve equal to the 

 sum of the depths be- 

 low it. Of course, if 

 there is any systematic 

 error running through- 

 out the work and always 

 in the same direction, 

 this method will not 

 detect it. 



If the expansion 

 per 1 were the same 

 throughout the range, 

 the curve would be a 

 straight line. Regnault 

 found, however, as 

 Dulong and Petit had 



1015 



.JO/0 



. -1005 



100 



1000 



FIG. 24. Graphic Method of Determining Results. 



_ already observed, that the line bends 



slightly upwards, that is, that the co-efficient of expansion slightly 

 increases. 



A constant co-efficient of expansion would be represented by 



A T = aT. 

 The slight bending upward may be represented nearly by taking 



and Regnault, from his diagram, found that 



a =-00017905 

 = 0000000252. 



Regnault's results have since been studied by others who have sought to 

 obtain formula more nearly representing his observations, but the differ- 



