758 MR J. D. HAMILTON DICKSON ON 



the shear-method, with enlarged scale, the multiplier being 4. This sheared curve is 

 the A-curve in fig. 9. The mid-points of seven chords parallel to the short line a on the 

 diagram were determined and plotted below a. They show a remarkably good straight 

 line without any slope. A second series of five mid-points of chords parallel to the short 

 line b were next determined, and were found to be so closely parallel to the a-locus 

 that it was justifiable to assume the curve to be a parabola with vertical axis. On this 

 basis the equation of the closest parabola was calculated by least squares from seventeen 

 of the thirty recorded observations, and gave 



(V + 270162569) 2 = 201757894(E + 36118-8720) . . . (36) 



Hence the equation of the (straight) Tait-line is 



<IE 2 (^ + 270-162569) 



dt ~ 2-01757894 ..... (37) 



These may be put in the forms, more convenient for calculation, 



E= -36118-8720 + -495643640 2 .... (38) 



where 



= /! + 270-162569 ...... (39) 



and 



dE/dt= -991287270, 

 or, in the usual form, 



dE/dt= -99128727* + 267-80864 ..... (40) 



The sum of the errors was + 8 '974 — 8 "974 verifying the calculation. From these errors 

 the probable error was found to be ±2*27 micro-volts, the range of measurement 

 extending over 624 micro- volts. 



The calculated sheared curve and parabola as well as the Tait-line are shown as 

 the B-curves in fig. 9. The vertex of the parabola can be shown on the diagram ; 

 it is at £=-270 '16°, E= -36118" 9. The observations are marked along the 

 B-parabola by means of small crosses. 



Cadmium. 



The curve of this metal presented a very marked deviation from a vertical parabola. 



The A-curve was drawn to the scale 1 mm. = 1° C. = 2 micro-volts ; the co-ordinates used 



E 

 were T = t + 200, H = — - + 200. To determine the slope of the axis with these 



co-ordinates, a transparent celluloid strip of rectangular shape, about 5 cm. broad, on 

 which was engraved one metre divided into half-millimetres, was laid so that the main 

 line marked on the scale took up sixteen successive parallel positions, thus selecting sixteen 

 parallel chords. In fig. 10 the successive positions of the edge of the celluloid scale 

 are indicated by the series of pairs of numbers 2, 2 ; 3, 3 ; . . . the first position being 

 marked by the two arrow-heads. These chords were inclined to the axis of temperature 



at an angle tan -1 — — , chosen because it was nearly the slope of the line joining the 



o 1 (J 



