28 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



and 5. The experimental values of the changes of volume at 20° in- 

 tervals were first plotted. A represents the change from 20° to 40°, B 

 the change from 20° to 60° (obtained by adding the change 40°-60° to 

 the change 20°-40°) and C the change 20° to 80°. The origin was now 

 connected to C by a straight line (this was done actually by a compu- 



20' 



40° 60° 



Temperature 



80° 



Figure 4. Shows the first step in 

 finding the change of volume at inter- 

 vals of 10° and the thermal expansion 

 from the readings of the volumes at 

 20° intervals. The heavy line shows 

 what the volume would be if the rela- 

 tion between volume and temperature 

 were linear. 



40° 60° 



Temperature 



Figure 5. Second step in finding 

 change of volume at 10° intervals and 

 the thermal expansion. The point A' 

 is the difference between the point A 

 of Figure 4 and the straight line. The 

 ordinates of this curve at interme- 

 diate points, when added to the 

 ordinates given by the straight line 

 of Figure 4 at corresponding points, 

 give the volume at intermediate 

 points. The slope at A' when added 

 to the slope of the straight line of Fig- 

 ure 4, gives the thermal expansion at 

 40°, for example. 



tation, not graphically) and the differences between the points 0, A, B, 

 and C and this straight line were plotted on another diagram, Figure 5, 

 on a larger scale. A smooth curve was drawn through these four points ; 

 from this curve the ordinates were read at the intermediate intervals 

 of 10°, and combined with the straight line values of Figure 4 to give 

 the volume at the temperature in question. The thermal dilatation 

 at any temperature, 40° for example, was found by adding to the 

 slope of the straight line OC the slope determined graphically at the 

 point A' of Figure 5. 



This method was also applied in determining the dilatation at 

 atmospheric pressure. An alternative method would have been by 

 differentiating the power series of Landolt and Bornstein for volume 

 as a function of temperature. The graphical method was thought 

 preferable, however, because a power series may often reproduce 

 the experimental points with greater fidelity than the slope of the 

 experimental curve. 



The dilatation, computed in this way, was transferred directly to 

 tables, and from the tables the curves were drawn which are given later 



