768 MR J. D. HAMILTON DICKSON ON 



of comparison. The equation of this line, calculated by least squares from the eleven 

 observed values of dE/dt, was 



f = 6^77^ +315 ' 6202 )' ( 58 ) 



from which, by means of the corresponding observed values of E, the equation of the 



parabola was 



(t + 315-6202) 2 = 6-274770(E + 15936-3) .... (59) 



The errors between the observed values of E and those calculated from this equation lay 

 between + 0*85 and— 128 micro-volts, and the probable error was only ±0'43 micro- 

 volt, over a range of some 250 micro-volts. 



After another interval of three years, in 1903 a new and direct calculation of the 

 equation of the parabola was made, leading to 



(^ + 314-0942) 2 = 6-24463(E + 15868-074) .... (60) 



The errors between the observed values of E from which this equation was deduced, 

 and the values calculated from this equation, lay between +062 and —0*73, and gave 

 a probable error of only ±0*28 micro- volt. The curve B was drawn from this equation 

 (60) ; all the recorded observations are plotted along it, and show a remarkable agree- 

 ment with calculation. The corresponding equation of the Tait-line is 



^eWs^ 314 ' 09 * 2 * ■ ■ ■ • ■ < 61 > 



or, in the usual form, 



dE/dt = 100-59658 + 0-3202752* . .... (62) 



E being measured in C.G.S. units, and t in degrees centigrade from the freezing-point. 



As a further test of the absence of slope in the axis of the E.M.F. parabola, the 

 A-curve was sheared, graphically, from the line LM, inclined at an angle tan -1 5/6 with 

 the axis of t. The sheared curve is the Sh-curve on fig. 14. The mid-points of a 

 series of twelve chords of this curve, parallel to the axis of t, were measured, and 

 (except the 1st and 1 1th, which almost coincide with other two points on the diagram) 

 are plotted below the short line a to which they are parallel. These chords are 

 separated by 1000 C.G.S. units from each other, and the successive values of t, 

 beginning with that immediately below the short line a, are 



- 54°, - 54i°, - 54°, - 53f °, - 53|°, - 53J , - 53°, - 53°, - 52f °, - 52|°, - 531°, - 55°. 



The departure of any of these temperatures (excepting the last, which would be re- 

 jected by Chauvenet's criterion) from their mean is on an average less than the errors 

 of observation, so that, as far as these observations go, the axis must be taken as 

 vertical. 



Taking equation (59) as representing the A-curve, from which it was directly 

 derived, the focus of the A-curve is at the point t = — 3 1 5*6°, E = — 249'4 C.G.S. units, 

 and the equation of the directrix is E = - 31374* C.G.S. units. The focus and the 

 directrix are both shown on the diagram, and it will be found that any point on the 

 A-curve satisfies, with great accuracy, the statement that it is equidistant from the 



