EXPERIMENTAL STUDY OF HEAT LEAIL\GE. 789 



and the points plotted to determine it show that the accidental errors 

 were smaller for plug S than for any other plug (see Table IV and Fig. 

 12). There are several other plugs for which the ratio of the range of 

 extrapolation to the range of observation is less than for plug S, but, 

 as an inspection of Fig. 13 will show, the inferiority of plug S in this 

 respect in a comparison with any of these plugs is outweighed by its 

 marked superiority in one or both of the other two respects. 



In the case of plug S, as has already been stated, the difference 

 between the value of ix' at the highest flow and its value on the axis 



of - is only 1.3 per cent, of the latter. The extrapolation must there- 



fore be supposed to be so uncertain that the part of the extrapolated ix 

 which depends upon it is in error by 40 per cent, of itself, if one is to 

 believe that an error as great as 0.5 per cent, is involved from this 

 cause alone. A rough idea regarding the probability of a percentage 

 extrapolation error of this magnitude in the curve of plug S may be 

 obtained by considering the extrapolation errors of other plugs. 



If it is assumed that the constant A in equation (2a) is zero, all of 

 the deviation of any extrapolated ji from the true /z must be assigned 

 to extrapolation error, in the sense in which this expression has hereto- 

 fore been used. Now, whether the precision claimed for the ^ given 

 by plug S is allowed or not, we may certainly suppose that 3.18 repre- 

 sents the true value of ^x within, say, 2 per cent. — that is, that ^i 

 certainly lies somewhere between 3.15 and 3.21. For any plug, the 

 extrapolation error will then lie between 3.15 — //'o and 3.21 — /x'o, 

 where /x'o is the extrapolated ix. The percentage error of extrapola- 

 tion is 100 times the ratio of the difference between the true (x and /x'o 

 to the difference between jx'q and /x'o, where ix'-y is the apparent value of 

 the coefficient observed at the highest flow. Hence the percentage 

 error of extrapolation lies between 100 (3.15— )u'o)/(m'o— M'2) and 100 

 (3.21— /i'o)/(A''o— ^'2). The values of these limits may be calculated 

 from the data given in Table IV; they are found to be, for plug Al, 

 20 and 52 per cent.; for plug A2, 34 and 64 per cent.; for plug A3, 

 128 and 192 per cent.; for plug Ul, 320 and 560 per cent.; for plug 

 U2, 400 and 700 per cent. For the other plugs, /x'o lies too close to 

 3.18 for the calculations to have much significance. 



It is thus seen that, for an error as great as | per cent, to be present 

 in the ix obtained by extrapolating the plot of plug S, we must suppose 

 the percentage extrapolation error with this plug to be of the same 

 order of magnitude as with plugs Al and A2 and from a third to a 

 fifth as large as with plug A3. One is justified in believing that the 



