THERMAL CONDUCTIVITY AND SPECIFIC HEAT OF MANGANESE-STEEL. 951 



of the curve, neither was applicable throughout its whole length with that exactness 

 which is necessary. Accordingly, the curve was treated in sections, each beginning with 

 a point corresponding to one of the holes in the bar, and terminating in another corre- 

 sponding to the next hole. Each part of the curve was, by addition to or subtraction 

 from its ordinates, converted into a logarithmic. From a comparison of the observed 

 and calculated values of v, it was found that the formula for these separate sections 

 represented curves having a slightly greater curvature than the observational curve, and 

 that the calculated numbers agreed better with the observed in the middle of each 



section. Hence the values of -=- were nearer the truth when found for the middle of each 



ax 



section, were too high for the higher values of x, and too low for the lower values. But 



dv 



were 



by making the sections separately treated overlap one another, three values of 



obtained ; one too high, another too low ; and a third, which always lay between these 

 two, and was obviously near the true value. 



It must be noted that the data from which the constants in the empirical formula? 

 were obtained were the ordinates of points merely on the curve — not those particular 

 points given directly by experiment. But the fact that the observations agreed remark- 

 ably with each other, and that by using different temperatures at the source of heat, a 

 considerable number of points were given directly by experiment, and all lying well on 

 the curve, justifies the use of such points for data. 



The experiments on the cooling of the short bar were carried out, and also reduced 

 in the usual manner. Hence little remark on this point is necessary, save the observa- 

 tion that the curve of rates of cooling at different excesses of temperature exhibited no 

 inclination to fall away, or show any point of contrary flexure. This, of course, is due 

 to the precaution of raising the short bar to a temperature considerably higher than 

 what is actually required to observe the cooling at any particular temperature excess 

 reached by any of the thermometers in the long bar. 



Final Results. — 



Rates of Cooling of Short Manganese-Steel Bar. 



Temperature 

 Excess. 



Eate of Cooling. 



Temperature 

 Excess. 



Rate of Cooling. 



5 



005 



110 



1-55 



10 



010 



120 



1-73 



20 



021 



130 



1-92 



30 



033 



140 



208 



40 



045 



150 



2-27 



50 



0-58 



160 



246 



60 



073 



170 



2-67 



70 



092 



180 



291 



80 



104 



190 



314 



90 



123 



200 



337 



100 



139 





1 



