THERMO-ELECTRIC DIAGRAM FROM - 200° C. TO 100° C. 



743 



where n was generally 200, and h and k were 200, or some such simple number. The 

 unit of T was always taken horizontally and represented by 1 mm. ; the unit of H was 

 represented vertically by 1 mm. The rest of the process may be exemplified by 

 platinum (Callendar's) the first metal examined. 



Platinum (Callendar's). 

 The 1898 calculation, fig. 3. The complete set of twenty-nine platinum tempera- 

 tures was reduced to centigrade degrees by the Table already referred to. From these 

 and the recorded values of Dewar and Fleming's E, were calculated 



T = * + 200, H = E/200 + 250. . . . -(4,5) 



The whole series of twenty-nine observations was plotted, and a curve drawn carefully 

 among the points in the manner previously described. The mid-points of fifteen chords 

 parallel to the axis of T were noted, and are shown on the A-curve above the short line 

 a to which they are parallel. As these points lay very closely on one straight line, what 

 was judged to be the nearest line to them was drawn, and on it the two points P, Q, 



at a distance of some 460 mm., were noted. The co-ordinates of P are, T=110, 

 H = 238; and of Q are, T = 140, H= -218 ; whence cot &> = 456/30 = 15 "20. 



In fig. 2, PA is the curve, A the vertex, AM the axis making the angle <*> with the 

 ordinate AB of the vertex ; PM is perpendicular to AM, and PN to OT. Puttino- 



OB = a, ON = T, and u> for tan w, 

 BA = k, NP = H, 



the curve is PM 2 =p.AM, where p is a constant. Substituting for PM, and AM, their 

 values in terms of T, H, this equation becomes 



{(T + HoS)-(a + A;oi)} 2 = i ;'{(/ 1 ;-ac6)-(H-Toi)}: . . (6) 



or writing 



and 



U = T + Bw = OG ; and u = a + M = OX ; 

 V=H-Tw = OF; u = &-ac6 = OY;J 



} • 



on expanding, it takes the form 

 where 



p = p sec (u ; 

 Ux-Vy -z = W 



x=2u, y=p, z = u 2 -p'v. andoi = 



"20 



(7) 



(8) 

 (9) 



(10) 



