HALL. — THERMAL AND ELECTRICAL EFFECTS IN SOFT IRON. 35 



nent temperature gradient of about 0.1° per centimeter from the ends 

 toward the middle of the bars. Under the same conditions, observations 

 made with the junctions which are attached to the guard-ring bars (see Fig- 

 ure 4) indicate that the mean temperature at the outer surface of the guard- 

 ring, for the 16 cm. corresponding to the distance between sections KN 

 and MP of the main bars, is approximately 4.5° below the temperature 

 of the boiling water in which the ends of a and ft are immersed. Taking 

 the mean temperature of the main bars in this case for the stretch between 

 section KJV nud section MP as 0.3° below the temperature of the water, 

 which in view of all the observations seems a reasonable estimate, we 

 get 4.2° as the mean difference of temperature maintaining lateral flow 

 of heat, a flow sufficient to maintain a gradient of 0.106 D per centimeter 

 along each bar toward the middle at both of the end sections. The 

 amount of heat thus transmitted per second is about 0.0242 calorie from 

 each bar. 



The lateral loss from each bar when one end is hot and the other cold 

 is probably considerably less than half this amount, as the difference of 

 temperature between corresponding points on the main bars and the 

 guard-ring bars is in this case apparently less than 2 D ; but even this 

 diminished flow is greater than the whole Thomson effect heat, and would 

 be very serious indeed if it were not very nearly the same from both 

 bars. The warmer bar being, according to the estimate already made 

 for (t a — t b ), about 0.21 warmer than the other, the excess of lateral flow 

 from the warmer bar may be estimated as 0.0242 X (0.21 -f- 4.2) calorie 

 per second. This is 0.001209 calorie per second, and the value found for 

 q in equation (6) should be increased by one half this amount, which will 

 give as our final value 

 (7) q = 0.00478.* 



To find <r, the mean amount of heat produced per second by sending 

 10 amperes, 1 c. g. s. absolute unit of current, through a temperature 

 interval of 1° downward in the region between 13.0° and 90. 3 J , we have 



o- = - q -T- 2.515 x (90.3 — 13.0) = — 0.0000246. 



If we assume that the heat generated or absorbed per second by a given 

 current flowing through an interval of 1° is proportional to the absolute 

 temperature of the metal at the point considered, — that is, if we assume 

 that the line representing iron on the ordinary thermo-electric diagram 



* The value of q would be 0.00183, if —0.0003 had been takeu as the tempera- 

 ture coefficient of thermal conductivity. See p. 33. 



