EXPERIMENTAL STUDY OF HEAT LEAKAGE. 769 



the data on which these plots are based, together with certain other 

 significant data. 



2°. The assumption is that .1 = 0. The confidence one feels in 

 the correctness of this assumption is based on the fact that to deny it 

 is to assert that 6Q, the heat leak per unit time, contains a term which 

 is proportional to fAp. As will appear later (see equation (4) and 

 Table II) this is the same thing as saying that dQ contains a term 

 approximately proportional to {Ap)^^^ (or to /^) in the case of axial 

 flow plugs, and to {ApY^'^ (or to/''^^) in the case of radial flow plugs. 

 Now the probability of the existence of an appreciable heat leak of 

 this sort is, on the face of things, extremely slight, because AT is 

 always at least roughly proportional to A^ (see Figs. 15 and 16) and 

 it is hardly credible that there can be any part of 8Q which increases 

 more rapidly — 50 to 75 per cent, more rapidly — than A T. In 

 putting A = we are therefore not merely making an assumption 

 which seems the most plausible of several alternative ones; we are, 

 on the contrary-, unable reasonably to make any other assumption. 



If A is zero, n may be calculated from any point on the line men- 

 tioned above by adding the amount B/f to the ordinate at this point. 

 Obviously the easiest method of doing this is to extrapolate the line 

 to the axis 1// = 0. This 'extrapolation to infinite flow' presupposes 

 nothing whatever as to the practicability, or even the theoretical pos- 

 sibility, of obtaining an ' infinite flow ' of steam, or any other flow lying 

 outside the experimental range. It is merely a graphical method of 

 arriving at the value of /x which is necessarily involved in the straight- 

 ness of the line and the absence of any part of 8Q proportional to fAp. 



It is consequently necessary to establish only the fact that the graph 

 is truly rectilinear over any range of observation, however short, in 

 order to avail one's self of this method of elimination. For example, 

 if the entire range of observation included a portion known to be recti- 

 linear, with a piece of curved graph at one or both ends, the latter 

 could be entirely ignored. But as a practical matter, it is possible 

 to be reasonably certain that the graph is really straight over any 

 range only by observing that it is straight, within experimental error, 

 over a reasonably extended range of observation. It is easy to imagine 



that terms of higher orders in might be present in the right hand 



side of equation (2a), and that these terms, although having so com- 

 paratively insignificant an effect within the range of observation as to 

 escape detection if the range is small, might nevertheless seriously 



