THERMO-ELECTRIC DIAGRAM FROM -200° C. TO 100° C. 755 



is the locus of mid-points of chords parallel to PER, of the original experimental curve 

 QS, and is therefore parallel to the axis of QS. The slope of the axis is the angle 

 LMK = 41° 59' ; it is given by 



whence 



, M'K M'M MK 6 

 C0tu, = KL = KL + KL = 5 + C0t 



cot " = ,ooL OK - 1-2 = 2-3130028 - 1-2 

 A32638D 



= 1-1130028. .... (31) 



with this value of cot o a final equation for QS was calculated by least squares from 16 

 of the recorded 3 1 observations. The co-ordinates used were 



T = * + 200, and H = ^ + 300, 

 and the equation found was 



( T+ r™- ur6869 ^ • • (32) 



which may be put in the more convenient form for use — 



F 

 2qq = 1238-2151 + 1T13003(9 -88-87935 J8 . . . . . (33) 



where 



(9 = 324-07083-!! ..... (34) 



Hence the equation of the Tait-line is 



dE 8887-935 



w = - 222-6006 + -^r- • ■ ■ (35) 



The sum of the errors was + 4'9314 — 49310, thus verifying the accuracy of the 

 calculation. These gave a probable error of only ± 1 '24 micro- volts over a range of 

 700 micro-volts. 



On fig. 7 the B-parabola, calculated from equation (33) is shown, and along it the 

 observations are plotted by means of small crosses. The comparison of the upper end 

 of this curve with the curves C and D is instructive as showing how the increase of the 

 assumed angle of slope has finally led to complete coincidence between theory and 

 observation along the whole range of the observations. The vertex of the parabola 

 lies within the observations, at the point t= — 164'03°, E= — 36466. 



The Tait-line representing equation (35) is shown with the B-curves ; and along it 

 the early measured values dE/dt (given in Table VI.), on which the first calculation was 

 based, are marked by small circles. These small circles show how easily it was possible 

 to assume their locus to be a straight line, and therefore that the parabola was vertical. 

 In fact the Tait-line itself, up to about 25° C, is fairly straight, and might even help to 

 bear out the illusion. But here, again, the curve is a cubical hyperbola. Its form is 

 shown in fig. 8, also its two asymptotes FG, HGH 7 ; the former being dE/dt = - 222'6, 

 the latter t= 3241°. The only portion of the curve associated with these observations 

 is the full-line portion AB. Parts of the asymptotes are shown also on fig. 7. 



