APPENDIX 



343 



FUNCTIONALITY 



If we pour some mercury into a U-tube closed at 

 one end, the air in this end will be contained in a closed 

 vessel under pressure. We can increase the pressure 

 by pouring more mercury into the open end of the tube. 

 We can measure the volume of the air by measuring 

 the length of the tube which it occupies. We can 

 measure the pressure on this air by measuring the 

 difference of length of the mercury in the two limbs 

 of the tube. By taking 

 all necessary precau- 

 tions we shall find that 

 for each value which 

 the pressure attains 

 there is a correspond- 

 ing value of the volume 

 of the air. 



We thus find the 

 pressure values, p^, pi, 

 pa, p4, pb, etc., and the 

 corresponding volumes, 

 Vu V2, V3, Vi, v„ etc., 



and we may then plot these values so as to make a 

 graph. 



In this figure the values represented along the 

 horizontal axis are pressure-values, and those repre- 

 sented along the vertical axis are volume- values. We 

 have so made the experiment that we can make the 

 pressure- values whatever we choose — let us call them 

 the values of the independent variable or argument. 

 For each value of the pressure, or argument, there is 

 a corresponding value of the volume, which depends 

 on the pressure — let us call these values of the volume 

 values of the dependent variable or function. 



Fig. 27. 



