ON THE ABSOLUTE EXPANSION OF MERCURY. 25 



Taking the observations above 100 C., the mean deviation of the values of the mean 

 ,-,///,/,,,/ ,,f .\|.;Hivi,,n fVi.ni tli.- t<ii-iiiiil:i U 15, \\lii--li corresponds t" :m ..uli-r "I' 

 accuracy of 1 in 12,000. The differences between the observed and calculated values 

 of the expansion itself are of the same relative order, and increase in absolute 

 magnitude, as one would naturally expect, with increase of temperature. 



None of the observations at 100 C. or below differ from the formula by so much as 

 0'002 cm. or 0'01 C. Only one of the observations above 100 C. differs from the 

 formula by as much as 1 in 8,500. We may fairly conclude that the formula 

 represents the results with an order of accuracy of 0'01 C. at temperatures l>elow 

 100 C., and with an order of accuracy of 1 in 10,000 above 100 C. Since positive 

 and negative differences occur almost alternately, and are little, if at all, greater than 

 might naturally lie expected from the limits of accuracy of the various readings, it 

 does not appear that any great advantage could l>e gained by the adoption of a more 

 complicated formula, or by any more elaborate reduction >i rr|>etition of the 

 experiments. 



The mean deviation of the individual observations at each point is about twice as 

 great as the deviation of the mean results from the formula. The individual 

 observations are affected by accidental errors of refraction through the glass of the 

 gauge tubes, and by errors of lag, which would disappear to some extent in the 

 means. Correction for lag would have made the observations agree with each other 

 much better in most cases, but the correction could not always be applied with 

 certainty, and it was therefore preferably omitted from the tables. 



10. Comparison with Previous Results. 



It may be of interest to compare the results of the present investigation, as 

 expressed by formula (8), with some of the formula? which have previously been 

 employed to represent the expansion of mercury. 



REGNAULT assumed a linear formula for the mean coefficient, namely, 



O a = {179007 + 2523(^/100)} x 10" 9 . 



He appears to have relied chiefly on the observations at the higher temperatures, and 

 the formula does not represent his ol>servations satisfactorily at temperatures Ijelow 

 '150C. 



BKOCH, in reducing RKGXAULT'S results, assumed a panilx>lic formula of the same 

 type as formula (8) for the mean coefficient. He also introduced a correction for the 

 conduction of heat along the cross tubes, which were not quite horizontal in 

 1 1 KUNAULT'S fourth series of observations, in order to reconcile the results of the 

 fourth series with those of the first three. The formula deduced by BROCH was as 

 follows : 



n<*i = {I817920+175(f/100) + 35ir6(?/100) s } x lO' 10 . 



VOL. COXI. A. E 



