66 Professors Ayrton and Perry on the 



specially noticeable in the early part of the expansion-curves 

 of gas-engine diagrams. 



It is further to be remarked that the vibration of the indi- 

 cator-spring is very visible in the expansion part, because we 

 have every reason to believe that the expansion part ought to 

 have no sinuosities ; but it is our belief that this vibration has 

 its effect on the explosion part of the curve as well, and that 

 it is of the utmost importance to find some means of elimina- 

 ting the effects produced by these vibrations of the indicator- 

 spring. 



In our communication to the Journal of the Society of 

 Telegraph Engineers, p. 391, vol. v. (1876), we showed how 

 to eliminate such vibrations in any case where the effect to be 

 measured followed a regular law of increase or diminution,- as 

 in the case of the expansion part of this indicator-diagram. 

 We have not yet sufficient information to enable us to employ 

 this method on the explosion part. 



The rule which we arrived at is as follows : — Draw two 

 curves, A and B, through the highest and lowest points of the 

 wavy curve which represents the actual observations : draw 

 ordinates : the points of bisection of the parts of the ordinates 

 intercepted between A and B lie on the correct curve. 



6. Empirical Formula for the whole Diagram. — Now, inas- 

 much as the compression and expansion parts of all the curves 

 follow the same laws, it would seem to be important to obtain 

 one general formula for all the diagrams with one or more 

 variable parameters. We have found that when we produce 

 the expansion-curve (using formula 1), as shown at B M (fig. 1), 

 and when we divide the pressure Q K at any part of the stroke 

 by the corresponding ordinate L E of the expansion-curve, 

 doing this for many parts of the stroke, we get the ordinate of 

 an interesting curve. We have done this for the four dia- 

 grams of fig. 1, and obtain the four curves A Q B D, AECD, 

 A.FD, A G H of fig. 3. From a study of these curves, which 

 are nearly formed of straight lines, it will be found that the 

 ignition and expansion parts of any diagram satisfy approxi- 

 mately the law 



p = U5'5r v479 {K / + nX-^( / c-n\y + s\. . . (3) 



The smaller the value of s the more nearly do the curves of 

 fig. 3 approach straight lines. In our present case X= I— 0*889, 

 #•/ = 0-6343, *=0*3637; 5=0*0087, and n has different values 

 for the four diagrams. These constants are evidently easily 

 calculated from any diagrams. For the curve shown as 

 A B C D in fig. 1 (PI. III.) the value of n is 2*2876. Using this 

 value and calculating p for the following values of I, we have 



