746 MR J. D. HAMILTON DICKSON ON 



or already explained ; the suffix c refers to calculated values, the suffix o to observed 

 values. The sum of the errors is + 7 '55 — 7 "58, which, being nearly nil, may be taken 

 as verifying the calculation. Hence is deduced the probable error ±1*33 ; that is, over 

 a range of temperature of 300 degrees and for electromotive forces extending from 

 — 435 micro-volts up to +128 micro-volts and back again to — 162 micro-volts, alto- 

 gether some 800 micro-volts, the probable error is only db2'7 micro-volts, thus showing 

 satisfactory agreement between observation and calculation. 



Equation (6) may, by means of the results in (12), be written 



(T + j^- 139-28654) 2 = 90-208406 (^-H + 304-9167o) . . . (15) 



For purposes of calculation it is preferable to rearrange it so as to give the value of 

 E explicitly. Substituting from equations (4, 5), after some reductions, we get 



E=- 2318743-64 -3040-* + 112812-36 VC + 422.-6022) . . . (16) 



or, in a still more convenient form, 



E= -1034032-96- 3040- 0+112812-36 ^0 ■ • • • (17) 



where 



= * + 422-6O22 .... (18) 



Hence we get the equation of the Tait-line, namely — 



It will be noticed that the Tait-line is a cubical hyperbola ; its equation may be 



written 



(rfE/^ + 3040-) 2 (i + 422-6022) = (56406-18) 2 .... (20) 



The general form of this curve is shown in fig. 5. It has two asymptotes C D and 

 E F, and two equal branches, one above, the other below, C D, neither of which crosses 

 E F. The particular portion of this curve associated with these observations is the con- 

 tinuous part A B. The asymptote E F is at the quasi-temperature — 422"6° C, and 

 C D is the line whose ordinate dE/dt has the value — 3040*. 



In 1908 an entirely new calculation was made for this metal from another " plot" of 

 the observations. To determine the parameter of the parabola, the co-ordinates of its 

 vertex, and also the slope of the axis by the method of least squares, was a labour of 

 such magnitude that, meanwhile, one did not feel justified in carrying it out. For- 

 tunately, it was possible to measure the slope of the axis with great accuracy from the 

 experimental curve, and I decided to accept the value thus obtained as satisfactory. 

 The new diagram, fig. 4, was drawn to the same scale as formerly. Nine parallel chords of 

 the A-curve were drawn, making an inclination with the axis of T whose tangent was '5, 

 an inclination easily observed on the millimetre paper. On marking the mid-points of 

 these chords, they were found to lie very closely on one straight line. They were dis- 

 tributed over a length of 170 mm., the last being about 22 mm. from the vertex, and 

 the first at the widest attainable portion of the curve. Over these points was laid a 



