764 



MR J. D. HAMILTON DICKSON ON 



Nickel. 



The range of this metal being unusually great, a first attempt was made to find its 

 curve by plotting E/800 to t. The arc thus obtained proved on trial to be too long 

 compared with its curvature to allow of its nature being determined geometrically. 

 Accordingly, the method of shearing was employed (it was devised to meet the case 

 of this metal). The co-ordinates used were 



E 20T 



T-* + S0O,H--j + : s 



1000. 



The observations plotted with these co-ordinates gave the sheared A-curve in fig. 12. 

 From this curve three sets of mid-points of parallel chords were directly observed ; 

 these sets of chords (as indicated by the short lines a, b, c, on the diagram to which 

 they were parallel) made angles with the axis of temperature whose tangents were 

 respectively + "4, 0, — '4, three values easily read off from the millimetre paper. These 

 sets of mid-points are shown above the short lines a, b, c, respectively ; each showed a 

 remarkably close approximation to lying on a straight line, and the three lines were 

 practically parallel, thus determining the curve to be a parabola. From the lowest 

 twenty of the 6-mid-points (those given in the annexed Table X. ), the straight line lying 

 closest to them was calculated by least squares. Its equation was found to be 



H + 47-75T = 7418-7216 ..... (48) 



Table X. 



H'.* 



T. 



H'.* 



T. 



150 



152-3 



250 



150-1 



160 



152-1 



260 



149-9 



170 



1517 



270 



149-9 



180 



151-6 



280 



149-6 



190 



151-5 



290 



149-5 



200 



151-1 



300 



149-2 



210 



150-9 



310 



149-1 



220 



150-5 



320 



148-8 



230 



150-4 



330 



148-2 



240 



150-2 



340 



148-1 



Hence the cotangent of the slope of the axis of the sheared curve is 4775, an angle of about 

 1° 12'. Employing this result with fifteen fairly evenly distributed observations of the 

 twenty-nine recorded, the parabola of closest contact was calculated and gave for its 

 equation 



(T + ^-^-154-31847) 2 = 67-0360642(' 47 ^r 5 -H + 372-389402) . . (49) 



whence, replacing T and H by their values in terms of t and E, and re-writing in a form 

 more suitable for calculation, it becomes 



E= -6,499,333-2 -10,883-36* + 540,430-14^ . • • ( 50 ) 



* H' is measured from an origin arbitrarily placed 250 below the axis of temperature, for convenience. 



