770 TRUEBLOOD. 



affect the value of n obtained by extrapolation. If one actually 

 obtained an experimental curve like that imagined above, with a 

 portion rectilinear within experimental errors and another, curved 

 portion nearer the 1// axis, for example, it would not be possible to 

 convince one's self that the true n could be obtained by extrapolating 

 the straight part. On the contrary, the extrapolation of the curved 

 line would certainly be expected to lead to the true value of //, and, if 

 it were possible to perform it, the process would differ in no essential 

 respect from the rectilinear extrapolation — that is, it would be 

 merely a mathematical process, with no implied assumption regarding 

 the possibility of physically realizing the inferred portion of the curve. 

 The true value of n is reached by the extrapolation because the terms 

 multiplying the first and higher powers of 1// vanish for f = oo ; and 

 the true value of fx could equally well be obtained by direct calculation 

 for any 1//, since the coefficients of these powers must theoretically 

 be known to perform the extrapolation. 



The results obtained by the rectilinear extrapolation of the data 

 obtained with several plugs are certainly considerably too small. 

 This is true of the axial flow plugs Al, A2 and A3 and of the radial flow 

 plugs Ul and U2. (Cf. Figs. 12 and 13.) In all of these cases, the 

 origin of the error must be ascribed to the presence of curvature which 

 either was ignored (because it was impossible to take account of it in 

 the extrapolation), as in plugs Ul and U2, or was not detectable, owing 

 to insufficient range of observation, as in plugs Al, A2 and A3. 



It is hardly to be supposed that any line would prove to be abso- 

 lutely straight, if it were possible to obtain results entirely free from 

 accidental error. Hence, although it is perfectly true that the recti- 

 linear extrapolation is merely a convenient method of obtaining a 

 result which could just as well be obtained by calculations confined 

 to the region of observation if the plotted line were known to be 

 strictly rectilinear, there will exist errors which may be properly called 

 extrapolation errors, in the sense that their magnitude will depend 

 upon the probability that the rectilinearity of the graph is a correct 

 inference from the data, and in the sense that this inference and the 

 value of fx deduced from it are the less certainly correct the greater the 

 accidental errors and the greater the ratio of the range of extrapolation 

 to the range of observation. It is also evident that, of two extrapola- 

 tions which are alike in the two respects just named, that one for which 

 the variation of the leak effect (8Q/f CpAjj) with the flow is the greater 

 — that is to say, that one for which the slope of the line is numerically 

 the greater — will lead to a less trustworthy value of yu than the other. 



