Gas-Engine Indicator-Diagram. 65 



If we assume the law of the expansion-curve to be 

 pl m constant, 



we have \ogp + mlogl=k ; so that when we plot log p and 

 log I on squared paper as coordinates of points, these points 

 ought to lie in a straight line if our assumption is correct. 

 Fig. 2 (PI. III.) shows how the points determined by the mea- 

 sured numbers lie ; and it is obvious that they lie very nearly 

 in a straight line. Taking the straight line which lies most 

 evenly among them, we find that it is defined by 



Hence 



Hence 



Now 



logZ=0'313, when log^l-7, 

 log £=0*0425, when logp = 2-l. 



1-7 + 0-310191=^ 

 2*1 + 0*0425 m=k. 



m= 1*479 and &=2\1629. 



log 145-5 = 2-1629. 

 Hence the law of expansion is 



p iv4 79=z 145.5 (!) 



In the same way we find that the law of the compression- 

 curve is 



p Z 1>304 =39-36 (2) 



It is obvious that the expansion-curve (1) is steeper than the 

 adiabatic, if we assume that the ratio of specific heats of the 

 fluid is 1*37, as the equation of the adiabatic curve is 



pl V3 7— constant. 



Again, the compression-curve (2) has less slope than the 

 adiabatic. 



5. Influence of Vibrations of the Indicator- spring. — We wish 

 to point out that it is exceedingly necessary, in obtaining the 

 law of expansion, to take many points in the curve, and, either 

 by using the algebraic method or by the use of squared paper, 

 to determine the most probable values of the constants. 

 Engineers are constantly in the habit of determining these 

 constants from measurements of the coordinates of two points 

 only in the curve, forgetting that the position of either point 

 may be much influenced by the vibrations of the spring of 

 the indicator. The sinuous shape of the expansion-curve is 

 Phil. Mag. S. 5. Vol. 18. No. 110. July 1884. F 



