THERMO-ELECTRIC DIAGRAM FROM -200° C. TO 100 C. 779 



measured directly from the A-curve. # As a corroboration of these values, use was made 

 of a property of an hyperbola, namely, that if m = tangent of the angle any series of 

 parallel chords makes with the transverse axis of the curve, and if mf = tangent of the 

 angle their bisecting diameter makes with the same axis, then mm' — b 2 /a 2 . The value 

 of (b/af is (2-28 1/7 -156) 2 , or '1017 ; the values of mm' are 



For the B line, tan 79° 36' x tan 1° 1' = '0967, 

 „ C „ tan 73° 50' x tan 1° 46'= -1040, 

 „ D „ tan 55° 24' x tan 4° 20' = -1098, 

 „ E „ tan 44° 5' x tan 6° 0'=-1018, 



of which the mean value is "1027. The close agreement of these numbers allows us 

 to consider the measurements as satisfactory. 



After a short calculation, the equation connecting E and t was reducible to the 

 following form, suitable for calculation, 



V = U + MJ(? + W) (77) 



where 



E 



7) = 77:7: + 360*736 micro-volts, 



£ = £-44*307 degrees cent, 

 mic. volts 



L = 2-97524 

 M = 4-84987 



deg. cent.' 

 mic. volts 



or, finally, 

 where 



deg. cent.' 

 jN 2 = 8414-05 (deg. cent.) 2 , 



E= -36073-6 + 297-524<9+ 484-987 7(^ + 8414-05) . . . (78) 



6 = ^-44-307 ..... (79) 



Hence the equation of the Tait-line is 



§- 297-524 + iSi - 9 m- w ^ mW) .... (80) 



From these equations (78, 79, 80) the B-curve of E.M.F. and the Tait-line were drawn. 

 The small crosses on the curve of E.M.F. mark the successive observations. From 

 + 100° to — 85° they practically lie on the curve ; at lower temperatures the coincidence 

 is not quite so good ; but there is no systematic error, and possibly, but for the reason 

 mentioned earlier in connection with the A-line of mid-points, this might have been 

 improved. A reduced sketch of this curve and its Tait-line (somewhat foreshortened) 

 is given below the B-curve. 



The equation of the Tait-line may be put in the form 



("7- W + a 2 ) = c 2 ! 2 (81) 



where 



£ = t- 44-307, a 2 = 841 4-05, 



_dE b = 297-524, 



f--^' c = 484-987. 



This is the equation of a quartic curve with two imaginary asymptotes parallel to the 



* See Note, p. 788. 



