262 PRINCIPLES OF THE MECHANICAL THEORY OF HEAT. 



when it occupies the position K, to be not constantly diminisTied, but to bo with- 

 drawn at suitable intervals, each time some ^— p, the pressure bearing upon the 



piston will then conform to the succession of values exhibited in the first column 

 of the followinjy table under D : 



If we denote by I the height of the piston above the floor, when it occupies its 

 position at the commencement, it Avill ascend by the succession of diminished press- 

 ures to the respective heights indicated in the second column. The height, 

 therefore, through which the piston rises at each succeeding diminution of press- 

 ure has the value given in the tliird column under li. 



Witliont sensible error, we can now assume that the pressure of the enclosed 

 mass of air acting upon the piston from beneath remains unaltered during its 

 ascent through one of the heiglits indicated in the third column under h. For this 

 pressure we may assign, as a first approximation, the value of D, standing in the 

 first column in the same horizontal row, which we must multiply into the cor- 

 responding value of h, in order to obtain the value of the worlv which is done 

 in the ascent of the piston through one of the divisions in question. The 

 products tlius obtained are grouped together in tlio last cohunn under /( D. 



The total work which is done wliile the piston rises, under the indicated 

 circumstances, from K to K', is therefore the sum of the values exhibited in the 

 last vertical row of the above table, namely, 



12 ■ 13 ■ 14 15"^ 16"^ 17"^ 18^ 19 

 The sum of the fractions standing between parentheses, which is most readily 

 obtained if they be changed into decimal fractions and then added, is 0.668, and 

 since iJ = 10333, while lis, 1 metre, there results for the total work L'=0.668' 

 10333 =6905^ metre-kilograms. 



This value of the total work is, however, manifestly too small; for we have 

 multiplied each of the heights consigned to the tliird column into the pressure 

 which acts against the under surface of the piston when it stands at the upper 

 end of the corresponding division. If we multiply each of the values of li into 

 the pressure which acts against the piston when it is at the lower end of tlie 

 division, the result will be 



V10^11^12 13^14^ 15^16^^17^18+19^^ ' 



-(!+!+' 



L'= 



^^+.^o)^^'- 



