HALL. — CONDUCTIVITY OF MILD STEEL. 293 



circuit wheu the other junctions were in use. Making this slight 

 change, and then taking the values of r as abscissas, and the values 

 of 8 as ordinates, we get the four determining points of curve A in 

 Figure 10. Taking various ordinates from this curve, and multiplying 

 each by the corresponding value of r, and, for convenience in plotting, 

 by 0.2, we get the determining points of the curve a. The area un- 

 der this curve is evidently 



0.2/8 Y.r'>idr, 







from which the value of A is at once obtained. In this case A = 4.52. 

 The mean of the observed values of 8 in the series under discussion 

 is 4.12. All this is for the case where the water above the disk was 

 warmer than that below the disk, on September 2. 



The same day another series of observations was made, with the 

 warmer stream beneath the disk. The curves B and h (Fig. 10) 

 have to do with this second series of observations. They give for the 

 value of A, 4.60. 



It is assumed in the subsequent calculations that A is equal to the 

 deflection which would be obtained from any pair of junctions on the 

 disk, one above and one below, if the difference of temperature were 

 made, for all values of r, equal to the difference between the mean 

 temperature of the whole upper face and the mean temperature of the 

 whole lower face of the steel disk. The validity of this assumption 

 will be discussed later. 



In the calculation presently to be made, the subscript 1 will have 

 reference to the circuit containing the junctions on the disk ; the sub- 

 script 2 will have reference to the circuit containing the copper- 

 German-silver junctions. 



The test for " sensitiveness " of the galvanometers, which has not 

 been described at length, was made by running the same current 

 through the two simultaneously. The " reduction factor," by which 

 the deflection in centimeters must be multiplied to give the strength 

 of this current in amperes, might be given for each galvanometer in 

 numerical terms ; but it will be evident that, for the calculation in 

 hand, it is necessary to know only the ratio of the two reduction fac- 

 tors, which is the reciprocal of the observed simultaneous deflections 

 of the two galvanometers in the sensitiveness test. 



In finding the value of m, allowance is made for the change of 

 capacity of the measuring flask with change of temperature of flask 

 and water. 



