32 MR. -T. H. GRINDLEY ON AN EXPERIMENTAL INVESTIGATION OF 



where T is the absolute temperature and v the specific volume of the wiredrawn gas 

 or vapour, and by differentiation we obtain 



(y), 



but by RANKINE'S* formula for the specific heat 



|-P 



Kp = constant T 



Jo 



we obtain by differentiation 



3K, 



Hence by comparing y and 8 we have the relation (a). The simplest method of 

 deducing the formula is by considering a small parallelogram on the p t diagram, 

 bounded by lines of free expansion and lines of constant pressure. 



We have therefore a very simple formula for checking the experimental results 

 just obtained, for if K P does not vary with the pressure as is indicated by Table V., 

 then the product CK P must be independent of the temperature at any particular 

 pressure. In order to obtain the values of K P at temperatures for which the cooling 

 effect is shown on Diagram 5, constant pressure curves were drawn on a diagram 

 having for abscissae absolute temperatures and for ordinates the values H z + ^P], 

 as explained on p. 27, Hj being the total heat of evaporation of the steam before 

 wiredrawing from a pressure P l and 0'016 representing the specific volume of water 

 at 32 F., the slopes of these curves giving the values of the specific heat under 

 constant pressure at any particular temperature and for the particular pressure at 

 which the curve is drawn. In this manner the results given in the Table VII. were 

 obtained and the necessary calculations made. 



From the fifth column of this table it will be seen that the product CK P is 

 practically independent of the temperature, and from the sixth column that it is also 

 independent of the pressure, i.e., CK P is constant between pressures of from 10 to 

 50 Ibs. per square inch, and between temperatures of 227 '5 and 327 '5 F. 



The mean value of CK P throughout this range of pressure and temperature is 

 0*2819. Outside this range of pressure it is impossible to give very accurate results, 

 but as no great and distinct variations actually appear, it would seem that the 

 constancy of CK P could be accepted beyond this range of pressure and temperature. 



The fact that the product CK P is practically constant is of very great importance, 

 as it will simplify many deductions from expressions in which CK P only occurs as a 

 product. 



For example, formula B just quoted gives a relation between v, T, C, and K P 



* BANKING'S ' Steam Engine,' p. 317. 



