738 MR J. D. HAMILTON DICKSON ON 



roughly parabolic, one naturally made the curvature everywhere of tlie same sign. But 

 it will easily be seen that this was by no means enough, especially if (as became 

 apparent) it was possible to maintain not only continuity of curvature but continuity of 

 change of curvature. By means of a hard, sharp-pointed pencil, and continued trials and 

 erasures, a clear, hard-black, thin-lined curve was obtained which satisfied the first 

 condition. By bringing the eye close to the paper and looking along the curve tan- 

 gentially, it was easily possible to detect stretches of curve, some of which were too 

 straight for the portions on either side, or too curved for the portions on either side ; 

 but it frequently required great care to decide whether, of two adjacent portions, one too 

 straight, the other too curved, the correction should be, increasing the curvature of the 

 former or decreasing that of the latter. An additional aid was gained in this matter by 

 looking tangentially at the curve through a magnifying glass (some 3 inches in diameter 

 and 8 inches in focal length, thus enabling a good stretch of the curve to be visible at 

 once) whose edge touched the curve while its plane was perpendicular to the curve at 

 the point of contact. By this device it was possible to train down the curve with great 

 precision to satisfy the second condition, and at the same time to make the line of the 

 curve very fine, its breadth not exceeding a hundredth of an inch. 



Some curves have simple geometrical properties which enable their natures to be 

 determined without knowing their characteristic points or lines, such as centre, foci, axes. 

 One such property possessed by conies is that the middle points of any series of parallel 

 chords lie on a straight line. In the present case, the curve had been drawn on milli- 

 metre paper, which I had tested to determine whether its ruling was consistent with 

 itself (I found it was not quite true), the opportunity of the parallel lines on the paper 

 offered an immediate series of parallel chords. On marking their mid-points they were 

 found to be very accurately collinear. The curve was therefore a conic. The parabola 

 possesses a further unique property — namely, that whatever the common direction of a 

 series of parallel chords may be, all the lines of mid-points are parallel and therefore 

 parallel to the axis of the curve. By means of this property I found that the curve was 

 a parabola (measurements being made to half a millimetre over distances varying from 

 55 to 300 millimetres), but that its axis was not parallel to the axis of E.M.F. This 

 departure from parallelism with the axis of E.M.F. was not great ; on the diagram each 

 mm. represented one degree of temperature horizontally, or two micro-volts vertically, 

 and the tangent of this angle of deviation lay between ^th and g^th, nevertheless it 

 was too marked to be neglected. 



On Tait's hypothesis, that the " specific heat of electricity " is proportional to the 

 absolute temperature, the curves of E.M.F. referred to temperature are parabolas with 

 their axes vertical, and the lines representing the thermo-electric power are straight 

 lines. Lines which represent thermo-electric power, whether straight or not, I propose 

 to call Tait-lines. By direct measurement from the observational curve obtained for 

 platinum (such curves will, in future, be referred to as the A-curves), data were found 

 lor the construction of the Tait-line. In getting these data, two things had to he 



