774 MR J. D. HAMILTON DICKSON ON 



The sum <»f the errors, being the differences between the observed values and those 

 calculated from equation (70), for the observations employed, was 11*16 — 11*14, which 

 verifies the correctness of the calculation. Hence the probable error was found to be only 

 ±2*58 micro-volts over a range extending from - 900 micro-volts up to 540 and back again 

 to 410. If we distribute the errors partly to E and partly to t, as the theory of error 

 points out, instead of entirely to E, the closeness between the curve of equation (70) — the 

 B-curve of E.M.F. — and the observations which are marked alongside by means of dots, 

 is very remarkable for this metal. Omitting the two exceptional observations at — 114° 

 and - 148°, the mean deviations of an observation are only *48 mm. on one side and *75 mm. 

 on the other side from the curve, the length of the curve being about 550 mm.* 



The highest point of the E.M.F. curve is at t= - 133-1°, E= 54178. The vertex 

 of this parabola is at t= —138*5°, E = 54068"; and the tangent of the angle its axis 

 makes with the axis of t is 2/19*372817. 



From equation (70) we get the equation of the Tait-line, namely, 



rfE bo »j K *o„ 62022*5714 



-—=-3874-5634 + ^— .... (71) 



dt JO v 



The Tait-line, as well as the curve of E.M.F., are shown among the B-curves ; to prevent 

 confusion, the temperature scale has not been entered for the B-sheared curve, but it is 

 easily determined from the A-sheared curve. 



Aluminium. 



The treatment of this metal was begun on squared paper divided into tenths of 

 an inch, and, as the original curves are given for each metal, this has not been transferred 

 to millimetre paper. In the free-hand A-curve the observations do not lie very close 

 to the curve between -75° and —120°; but, following the conditions under which 

 these free-hand curves have been drawn, namely, continuity of curvature and continuity 

 of change of curvature, it did not seem possible to draw the curve otherwise — in any 

 case, this is the actual curve first drawn. The test employed to determine the nature 

 of the curve was the same as before, namely, to examine if the mid-points of parallel 

 chords lay on a straight line. The mid-point of the longest possible chord is at a on 

 the diagram, fig. 18, and below it four other mid-points are marked. These show some 

 deflection from a straight line, but in the same sense in which the free-hand curve 

 departs from the observations, as already noted. Another geometrical property of the 

 curve was therefore employed to help to decide the matter, namely, that the intersection 

 of pairs of tangents at the extremities of parallel chords meet on the line of mid-points. 

 The tangents at A and B seemed to meet at b, and, as the line ab seemed fairly to suit 

 the conditions, it was accepted as giving the direction of the axis of the parabola. The 

 two points within small circles on this line were sufficiently far apart to give a close 

 determination of its inclination to the axis of E.M.F., and from them the tangent of this 

 angle w was found to be 65/80, or 13/16. 



* See Note, p. 788. 



