776 MR J. D. HAMILTON DICKSON ON 



From fifteen of the recorded twenty-nine observations, fairly evenly distributed, the 



equation of the curve was calculated by least squares. To simplify the calculations, the 



co-ordinates employed were 



T = t + 408, and H = E/100 + 100, 



and the equation connecting them was found to be 



(t-&-211-20145Y = 1H8-03269^T + H- 420-65845) . . . (72) 



or, in a form more suitable for use, 



E = 65765-844 + ^0-5960-965^/0 .... (73) 



where 



= ^+287-68268. ...... (74) 



The sum of the errors between the calculated and observed values of E.M.F. for the 

 temperatures employed was 5 "23 — 5*31, which, being practically zero, verified the cal- 

 culation ; and the corresponding probable error was ± '8 micro-volt, over a range 

 of 214 micro-volts extending from — 190° to + 100° C. 



The corresponding equation of the Tait-line is 



1 



dE 



16 



1 59-60965 



0( 



) dt ' 



13 



2 



J* ' 





dE_ 



dt ~ 



= 123-077 



2980-4825 



or 



dK 9,980-4R5!5 



(75) 



The B-curve of E.M.F. represents equation (73) within the range of experiment ; 

 the observations being shown by small crosses. The vertex V of the parabola is at 

 t= -74-91°, E = 5002-0 C.G.S. units. 



The Tait-line CD was plotted from equation (75). It has two branches, part of 

 the second being shown at EF ; but no physical meaning has been attached to this 

 second branch. In the case of a slant parabola, at some point there will be a vertical 

 tangent ; this is at t= — 2877°. The corresponding point on the Tait-line is at infinity ; 

 and, in fact, t= — 287'7° is the equation of an asymptote (shown at GrH) to the Tait- 

 line. This again corresponds with no known physical phenomenon, being at a tempera- 

 ture below the absolute zero. On the other hand, at some real temperature the parabola 

 has a tangent parallel to the axis of t ; this is at 298 7° C, where the Tait-line cuts the 

 axis of temperature — the neutral point with lead. Both upper and lower branches of 

 the Tait-line stretch towards infinity with increasing temperature, and approximate to 

 the asymptotic value 123'077, shown by the dotted line KL. The Tait-line is again a 

 cubic hyperbola. 



Antimony. 



The work for this metal was begun on inch-squared paper, as in the case of 

 aluminium, and this has been preserved. Of all the metals examined (except iron) this 

 gave the most trouble and has proved to be the most interesting. The A-curve on 



