APPENDIX 



345 



and the latter decrease is greater again than the 

 decrease from fg to v^. Evidently the rate of variation 

 of volume is not like the rate of variation of pressure, 

 that is, the same throughout, and when we look at the 

 graph we see that the rate of variation is greatest where 

 the slope of the curve is steepest. The latter is steepest 

 near the point a, less steep near the point b, and still 

 less steep near the point c. Now any small part of 

 the curve is indistinguishable from a straight line. Let 

 us draw a straight line 

 eei, which appears to 

 coincide with a small 

 part of the curve near 

 a, and similar straight 

 lines^i ,and ggi , which 

 also appear to coin- 

 cide with small parts 

 of the curve near b 

 and c. Then the 

 steepness of the curve 

 will be proportional 

 to the angles which 

 these straight lines 

 make with the axis op, and these angles are measured 



by their tangents, that is, by the ratio 



makes with op, 



Fig. 28. 



e^e 



—' which 

 oe 



the ratio 



is the tangent that 



^, and the ratio -^\ 



The point a on the curve corresponds with a 

 pressure a^ and a volume Un. The point b corre- 

 sponds with a pressure b^ and a volume bn, and 

 c with a pressure Ci and a volume Cn- The average 

 rate of variation of the volume of the gas, as 

 the pressure changes from a to c, is therefore 



