OF IRON, COPPER, AND GERMAN SILVER. 549 



Diagram 2 shows the degree of approximation to it in this work. With 

 the exception of that of German silver, the curves for the other bars did not 

 exhibit the result in question to the same extent. 



In connection with the consideration of the statical curve, it will be well to 

 compare in this respect the results of this work with those of Principal 

 Forbes and Prof. Tait. The curves for iron, according to these three 

 different sets of experiments, are shown in Diagram 1. From the disposition 

 of these curves one to another, it will be seen that (1), that given by Forbes 

 (marked F), shows a greater rate of change of temperature along the bar 

 than either of the other two ; (2) that my own experiments, i.e., on the nickel- 

 plated bar (marked M), show a slower rate of change than those of Prof. Tait 

 (marked T) ; (3) that all three agree with comparative closeness at the lower 

 temperatures. 



The first of these remarks is confirmed when the values of dvjdx at different 

 temperature excesses are plotted. The values which Forbes used are then seen 

 to be all greater than those used in the deduction of conductivity in this work ; 

 on the average they are about 10 per cent, larger. No details of this kind (i.e., 

 values of tangents used, &c.) are printed in Prof. Tait's paper, otherwise they 

 would have formed an interesting comparison. 



In the calculation of the tangents the values obtained by differentiation of 

 the formula representing the curve have mainly been relied upon, except at the 

 lower temperatures, where graphical measurements have been made and used. 

 But some allowance must be made for the discrepance between the calculated 

 and observed values of v. It was effected in this way. By the sign and 

 amount of the difference between these two values, it can be determined 

 whether at any given point the curve (by calculation), in bending away (below 

 Or above it) from the observational curve, makes the calculated values of dvjdx 

 too small or too great. By taking other values of the constants, a value of 

 dvjdx may be obtained with a probable error, at any given point, of opposite 

 sign to that obtained by the first value of the constants. Thus it is known 

 between what two limits lies the accurate value of the tangent at the given 

 point. 



Excepting the remark made that the value of the tangents graphically 

 measured agreed satisfactorily with the value calculated from the formula, 

 Forbes seems to have used alone, and without any such modification as is men- 

 tioned above, the values of dvjdx as they are given directly by one particular set 

 of values of the constants, — viz., that set which appeared to give the best 

 agreement with the observed temperature excess along the bar. Treating the 

 curve in sections, as he did, partly avoids the difficulty ; still, it cannot be 

 doubted that without any allowance of the kind mentioned, the calculated 

 values of the tangent to the curve, constrained as it is to pass through three 



