780 MR J. D. HAMILTON DICKSON ON 



axis of E.M.F. ; and two real asymptotes parallel to the axis of t whose equations are 



n = b zh c, or 



dE/dt = 782-51, and dE/dt= -187-46 .... (82) 



These are both shown on the reduced curve. 



It may be noted that between the temperatures of— 28° C. and + 107° C. (approxi- 

 mately) the Tait-line does not depart much in form from a straight line. The small 

 circles on the Tait-line are the points calculated from equation (80) by means of which 



the line was drawn. 



Silver. 



This was one of the earliest metals examined. A curve was drawn through the 

 plotted observations, and properties depending on the geometrical relations of the 

 parabola were employed to determine the focus and directrix, on the assumption that 

 the curve was a parabola. This curve is the A-curve of E.M.F. on fig. 20. The focus 

 was found to be outside of the diagram ; but the diagram was pinned to a large board, 

 the position of the focus marked, and the following measures were taken : — 



Temperature 



Distance from focus to 



Distance from directrix to 



t- 



point 



at temperature t. 



point at temperature t. 



-190° 





215 mm. 



215 mm. 



-100° 





301 „ 



300 „ 



0° 





430 „ 



430 „ 



50° 





507 „ 



507^ „ 



100° 





597 „ 



597 „ 



These amply justified the inference that the curve was a parabola, and (as it 

 happened) that its axis was vertical. 



Having at a later period devised the method of shear, it was applied to verify this 

 result. The above curve was sheared from the line CD which made an angle with the 

 axis of t whose tangent was 4/3 ; the ordinates thus obtained were multiplied by 3, and 

 the result is the sheared curve EF. The mid-points of a series of horizontal chords, 

 parallel to the short line a, were observed and marked on the diagram. They are 

 naturally a little uncertain, but the run of them does not justify any idea that they 

 indicate other than a vertical axis. From fourteen fairly evenly distributed observa- 

 tions the equation of the parabola was calculated by least squares. The co-ordinates 

 used were 



T = t + 200, and H = E/200 + 300 ; 



the equation that was obtained was 



(T + 200-7247) 2 = 541-45275 (H- 2-1510465) . . . (83) 



or, arranged for calculation, 



E= -5956979 + -3693766(9 2 . .... (84) 



where 



Q = t + 400-7247 ..... (85) 



The sum of the errors between the observed and calculated values of H was 5 '83 - 5 '89, 

 which verifies the correctness of the calculation. These gave a probable error of ±1*53 

 micro- volt over a range of some 760 micro-volts. 



