782 MR J. D. HAMILTON DICKSON ON 



From equation (84) we get the equation of the Tait-line, in this case a straight 



line, namely, 



dE/dt = 2 x -3693766(9 . ..... (86) 



or 



dE/dt = 296-03673 + -7387534* .... (87) 



The curve of E.M.F., which is given by equation (83), is shown as the B-curve on fig. 20, 

 and along with it is given the Tait-line. 



The Thermo-Electrio Diagram. 



From these calculations the thermo-electric diagram of fig. 21 was constructed, to 

 the scales marked upon it. This was completed on 7th July 1909. 



During the long period throughout which these calculations have extended, the 

 cause of the sloping parabolic axis has continually been a matter of research to me. 

 It seemed as if it were dependent on the lowness of the temperatures at which Dewar 

 and Fleming carried out their investigations, for no other observer had done otherwise 

 than take for granted that the Tait-lines were straight. Where this had not been 

 done, empiric formulas had been adopted, beginning with the first one proposed by 

 Avenarius ; and Professor Silas Holman had discussed all those proposed, and 

 suggested some new ones, of which one would be suitable for one set of observations 

 and another for another set. Professor Tait had suggested a run of successive arcs of 

 parabolas with varying parameters, but parallel axes, subject to the condition of common 

 tangency at the points of exchange, and had given formulas of connection for them ; 

 but these were mainly called forth by the quite anomalous performance of iron in the 

 first place, and later of nickel. His general conclusion was in favour of "parabolas 

 with their axes vertical " — which he " found by actual measurement of curves plotted 

 from experiment " to be the case within " the inevitable errors of experiment " for the 

 "junctions of any two of iron, cadmium, zinc, copper, silver, gold, lead, and some other 

 metals," and this :< within the range of mercury thermometer." In a note, added later, 

 he amplifies this to the case of " a curve symmetrical about a vertical axis " ; but at the 

 same time he fixes his mind on the parabola as the curve in question and goes on to 

 make a deduction from it. The deduction is that if the E.M.F. of one pair of metals be 

 plotted as ordinates to the E.M.F.s, taken at the same instants, of another pair of metals, 

 the resulting curve is also parabolic, but now the axis is no longer vertical. He proves 

 this immediately by referring to the case of a projectile in vacuo becoming subject to 

 a constant horizontal force, the resultant of which with gravity would still be a constant 

 force, but no longer vertical, and therefore the trajectory would be a parabola but also 

 no longer vertical. Clearly, if we start with two inclined parabolas, one giving abscissas 

 the other ordinates, these two will have a " resultant " — like Professor Tait's — but again 

 with a differently inclined axis. Hence his deduction does not militate against an 

 inclined axis. Now, while he prefers the parabola with the vertical axis — excluding 

 iron and nickel — he notes that when the range of temperature is great enough, " when 



