754 



MR J. D. HAMILTON DICKSON ON 



straight ; further, as the curve (scale, 1 mm. = 2 micro-volts) presented only a slight 

 concavity, no marked slope of the axis was visible. The equation of a vertical parabola 

 was therefore calculated by least squares ; but the result, while fairly satisfactory below 

 50° C, showed a systematic divergence between the observations and the curve above 

 this temperature (see fig. 7, C). In 1908 a new attempt was made to determine the 

 slope of the axis, but without success. On devising the " shear " process, recourse 

 was had to it with enlarged scale to settle the question. The enlargement of the 

 scale complicated matters, for while small divergences from a hand-drawn curve were 

 permissible (such as 2 or 3 mm.), with the scale enlarged eight times these became 

 16 or 24 mm., and it was quite a chance whether the truth could be obtained in 

 this way. However, by steering a moderate course, this trial gave distinct evidence 

 of slope, the cotangent of the angle being 2"665 (w = 20°40 / ). Nevertheless, there was 

 still the appearance of systematic divergence between the observations and the curve 

 at the higher temperatures, though not so much as before (see fig. 7, D) In this 

 case the shearing had been obtained by calculation from the E.M.F. and temperature 

 of each observation. A final attempt was made thus : The observations were plotted, 

 and a free-hand curve drawn through them in the manner previously described 

 (fig. 7, A-curve). Through a point E on the axis of E.M.F., chosen merely as a 

 convenient point, a line PER was drawn making an angle having an easily read 

 tangent, namely 6/5. Then the sheared curve was deduced directly from the diagram 

 by merely noting on the millimetre paper, as at 50°, the length PQ, and transferring 

 this length to the sheared position P'Q'. Such measures and transfers were made at 

 every 10° from - 190° to +100° C. Thus the original curve QS was sheared into the 

 position Q'S', and the straight line PE became P'E. The mid-points of a series of 

 twelve parallel chords of the sheared curve were then carefully observed and measured, 

 their positions being given in Table V., where 200E' is the E.M.F. These points were at 

 the same time plotted below the short line a which is parallel to the chords. By least 

 squares the nearest straight line M'L through these points has for its equation 



i + 0-4323385E' + 46-8766 = ..... (30) 



Table V. 



fC. 



E'. 



t'C. 



E'. 



-58-0 



27- 



-51-0 



8-0 



-56-5 



23- 



-490 



6-0 



-55-75 



19-5 



-48-5 



3-5 



-54-25 



16-5 



-47-5 



1-75 



-52-75 



13-5 



-46-5 



o- 



-52-0 



10-5 



-460 



-1-5 



If now all the sheared lines be wn-sheared to their original positions, M' will fall 

 back to M, while L will retain its position as it is on the line of no-shear. Thus ML 



