70 Professors Ayrton and Perry on the 



may be negative or positive, adding to it 7 times S T and 

 dividing by 7— 1, we obtain the ordinate q of the heat-curve. 

 Another method is to calculate q as given in (6), by actual 

 differentiation of p as given in (3). We have employed this 

 method, and believe that our result, in which the early part 

 of the curve E F (fig. 4) is less steep than there shown, is 

 probably more nearly true than what is given in fig. 4. We 

 do not put our result forward at present because there may be 

 a discontinuity in the explosion part of the curve, as Table VII. 

 shows that at X — '061 the empirical formula does not give the 

 observed pressure; and until we know how to eliminate vibra- 

 tional effects of the indicator-spring, we have preferred only 

 to publish the curve EFGH which has been obtained from 

 the actual diagram, the expansion part only having been cor- 

 rected for vibrations. As we know that the expansion part 

 follows a law 



p = K l~ m , 

 it is obvious that 



7 — m 



being proportional to the pressure. Now, comparing this 

 result with the part G H (fig. 4), we see that G H is not quite 

 correct, although determined from most careful measurements 

 of the indicator-diagram. We see here an illustration of the 

 great importance of obtaining a formula such as that given in 

 (3) for the shape of the indicator-diagram. 



9. Total Heat and Work of One Cycle. — The integral of q . dl 

 multiplied by the area A of the piston in square inches gives 

 the total heat received by the fluid during any part of the 

 stroke, and is evidently 



A! q -dl= ——r(p 2 l 2 —pih) + A\ p.dl. 



Taking from the diagram 



Pl = 44-5, l x = -889, 



^ 2 = 49-0, / 2 =2'089, 



so that l 2 — li = l'2 foot (/ 2 corresponds to the part of the stroke 

 at which the exhaust-valve opens), it is evident that 



Ch Ch 



\ £.^=169-5+l p.dl (7) 



Or if q m is the mean value of q during this portion of the 



