HALL. — CONDUCTIVITY OF MILD STEEL. 283 



True Difference of Error 



Temperature. 



1st case 28 + [^ejes - 24 + \_E{\., [^o],s - [E^^^ 



2d case 28 + IE{\._, - 24 + [^2]-24 [^J^s - \.E.{\^, 



Error of mean = ^ ([^i],3 - [^i].,,) + \ {^E;],, - \_E.;\^,) 



Similarly, the error of the mean at the higher temjjeratures is 



i ([^iJtO - [^1]C6) + h ([^2]70 - IE,-],,). 



If the "error of the mean" had been equally great at all observa- 

 tion stages on the thermometers, it would have affected the absolute 

 value of the result obtained for the sensitiveness of the copper-steel 

 thermo-electric element, but would have left unaiFected the ratio of 

 the sensitiveness at one temperature to that of any other temperature. 

 Calibration of the thermometers showed that the " error of the mean " 

 was not the same everywhere on the thermometers. The variation, 

 though small, was perceptible, and might, if neglected, make the in- 

 terval called 4° at one stage one half of one per cent greater or less 

 than the interval called 4° at another stage. This error would not be 

 very serious in view of the general character of the experiments if it 

 had its full effect ; but, in fact, the conclusion as to the conductivity 

 of the steel depended upon the ratio of the sensitiveness of the copper- 

 steel element at any temperature to that of the copper-German-silver 

 element at or near the same temperature. Both kinds of element 

 were calibrated by means of the same thermometers, and therefore 

 the chance that final error of any magnitude could result from neglect 

 of the errors of the thermometers is exceedingly small. Accord- 

 ingly, such errors were neglected, the thermometers being used as if 

 correct. 



The question of course arises whether the two junctions differed in 

 temperature just as much as the two thermometers did. It is no doubt 

 true, that, when temperatures much above those of the room were used, 

 each of the steel bars, several centimeters of which were exposed to 

 the air, was a little cooler at each end than the water flowing past it. 

 This difference was probably small, and must have been about the 

 same at each end. The disturbance, or inaccuracy, caused by it 

 should be smaller with the slender bar than with the other. Accorfl- 

 ingly the slender bar was used most of the time, and all the results 

 but one recorded in the following table were obtained with it. On 

 the last day of the observations on copper-steel junctions one of the 

 junctions on this bar broke. Then the thick bar was substituted for 



