610 PROCEEDINGS OF THE AMERICAN ACADEMY. 



ductivity in the main bars. During these observations there was no 

 electric current in these bars and the two were treated as one, in this 

 sense, that no attempt was made to determine the temperatures or 

 the gradients of temperature on the main bars singly, mean values 

 only being looked for. Accordingly, in what follows ta will indicate 

 the mean temperature of the two main bars in the cross-section a, 

 Qa will indicate the mean gradient of temperature of the two bars 

 at the same cross-section, etc. Similarly t'^ will indicate the mean 

 temperature of the guard-ring bars, 1, 6, 11, and 16, in the cross- 

 section a, etc. 



The general method followed in this phase of the investigation was 

 to establish practically fixed conditions of temperature, by keeping 

 the boilers in action several hours before the beginning of observations 

 for record, and then proceed substantially as follows : 



1. Data were taken from which the gradients of temperature g^ and 

 g, could be found. 



2. Data were taken from which the difference between the tempera- 

 ture of the main bars and the temperature of the guard-ring bars 

 could be found for each of the five cross- sections, a, b, c, d, e. These 

 data were obtained, in ways already sufficiently indicated, by means of 

 the thermo-electric couples, a^, fi,„ Gu, G^^, Giu, Gi6,„ etc. 



As the various junctions lying nominally in any given cross-section 

 do not strictly so lie, there is opportunity for very considerable errors 

 in the estimation of the temperature differences mentioned in (2) above. 

 It is possible to eliminate such errors almost wholly from the final re- 

 sult by making two complete sets of observations of the kinds indi- 

 cated in (1) and (2) above, one set with the a end of the apparatus, 

 the east end, the hotter and the other set with the e end, the west end, 

 the hotter. The first condition existed on February 7, and the second 

 condition on March 2 and 3. 



The following table exhibits the main data obtained from the two 

 sets of observations. The temperatures, t, given for points on the 

 main bars, were in some cases estimated from data obtained at other 

 times ; but the possible inaccuracy of these values cannot be a source 

 of important error. The columns headed (f-f) give the excess of tem- 

 perature of points on the main bars over nominally corresponding 

 points on the guard-ring bars. 



At the foot of each gradient column is given the difference of 

 gradient ; at the foot of each t column, the range of temperature ; at 

 the foot of each t-t' column, the mean value of the column. 



The values in the last three columns, which are mean values taken 

 from the preceding columns, are used in finding the temperature co- 



