742 



MR J. D. HAMILTON DICKSON ON 



axis of the "sheared" curve P'R'A'Q' with the axis of E.M.F., is easily found. Let A 

 be the point of PQ at which the tangent is parallel to BC. A will become the highest 

 point A' in the new curve P'A'Q' : let M be the mid-point of the chord of the curve 

 intercepted in BC, then, assuming the curve to be a parabola, AM is parallel to the axis 



H 









f\ 









' /CO 









/ 



Y 





A' 



\ 







R^ 



/ r 



K^f 





p / 





*A 





L 







V 



B 



N 1 M' 

 Fig. 1. 



H' 



of the curve : let the ordinate AK' cut BC in K and the " sheared " curve in A'. 

 Construct the rectangle MLK'M', and join A'M'. Then, on the same assumption, AM 

 will bisect all chords parallel to BC, and clearly A'M' will bisect all chords in the " sheared " 

 curve parallel to OT ; hence the " sheared" curve is a parabola also, and A'M' is parallel 

 to its axis. Then, if m be the tangent of the angle CBT, 



cot to = 



AL AK + KL 



ML' 



ML 



A'K' KL 



If the ordinates of the "sheared 

 relation becomes 



curve have to be increased in the ratio A : 1, tins 



COt a) 



cot a) = — r — (- m 

 A 



(1) 



This process is severe as a test of the truth of the theory, and, with the liberty we have 

 in the choice of A and 'in, allows us to give w such a magnitude as to be easily read in 

 any case. The process was applied with complete success to zinc and copper, both of 

 which, in the earliest attempts, appeared to give parabolas with no slope. With the 

 former metal the result was confirmed, while with the latter a great slope was discovered, 

 as well as the explanation of why the earlier attempt had failed. 



The general process of investigation was as follows : — 



Let E = electromotive force in C.Gr.S. units as recorded by Dewar and Fleming, and 



let t = centigrade temperature measured from the freezing point of water, and calculated, 



by means of the Table already referred to, from the recorded platinum temperature. To 



prevent the chance of any error in using the method of least squares, as each set of 



observations contained both positive and negative electromotive forces and tempera 1 u res, 



new co-ordinates were taken so as to make these quantities always positive. Thus, 1 put 



T=t + k (2) 



and 



K = E/n + h .,.,.. (3) 



