8 Palmer — Pressure Coefficient of Mercury Resistance. 



Combining these observations by the method of "Least 

 Squares " we have 



at 9° C. R = 12-4518 — -000414P 



at 100° C. R = 13-3999 — -000451P 



The lines on the chart have been drawn in accordance with 

 these equations, and it will be seen that the plotted points are 

 very nearly in coincidence with them. The values of R com- 

 puted by these formulae have been entered in the tables under 

 R' and the relative errors, from which the probable error of a 

 single observation has been found to be '008 ohms at 9° C. and 

 •012 ohms at 100° C, under R— R'. Hence the resistance 

 measurements are accurate to less than one-tenth of one per 

 cent and are as good as could be expected when it is remem- 

 bered that the uncertainty in determining the pressure is about 

 the same in magnitude and that it is impossible to entirely 

 prevent leakage when very high pressures are employed. 

 Furthermore small errors were probably introduced by the lag 

 in the indications of the mercurial thermometers behind the 

 actual temperature variations. Putting the above equations in 

 the form 



R.= R;(l+.j80P) 



where (3 is the increment to unit resistance caused by 

 one atmosphere increase in pressure, we have, after calculating 

 the probable error in the usual way from the sum of the squares- 

 of the errors, 



at 9° C. j3= — •00003324 + -00000014 



at 100° C. /3= — -00003367 ±'00000019 



Hence it follows at once that at any temperature 



(3 — — -0000332 — 5 X 10~ 9 1 



where the last term, owing to its extreme smallness, is probably 

 only approximately accurate. 



The difference between this result and that of Barus 

 (—•00003) is so small that it can be easily accounted for by the 

 slight impurities in the commercial mercury used by him. 

 Lenz's original paper is unfortunately inaccessible and the 

 account of it in the Beiblatter is meager. He used a tube 1*2 

 meters long filled at atmospheric pressure, and it is probable 

 that the very large coefficient (— -0002) obtained was due to the 

 imperfect removal of air bubbles from its inside walls, a source 

 of error having its maximum effect at the low pressures 

 employed by him. 



. The two series of observations marked by circles on the 

 chart, fig. 1, are so obviously affected by consistent errors that 

 thev have been left out of the calculations. The first was 



