THERMO-ELECTRIC DIAGRAMS. 305 



parabolic, e = at •}- bt^, where b is positive or negative, according 

 as the lines for the metals cut below or above the temperature of 

 the cold junction, and is equal to half the difference of the Thom- 

 son effects for the two metals. To determine a and b as accurately 

 as possible I worked it out for each series of observations by the 

 method of least squares. Thus a and b must be determined so that 

 2 (e — at — bt") is a minimum, the conditions being that 



e?2 , c?2 



— — = o and ~—j~ :=. o, i.e. : — 



da db 



^ et — a^ t" - b'2 f" = o 



'2, et" — a^ t'-" — b^ f- = 

 two equations which give a and b, but necessitate finding 2 et, 

 2 et",^ t^,^ t\^ t*. The finding of a and b from a dozen 

 observations takes about 90 minutes arithmetic. I took three or 

 more sets of observations on each junction examined, the mean 

 results being embodied in the following table and shown graphi- 

 cally in the diagram (see Plate IX.): — 



Aluminium — 52-7 + •2lt 



Tin — 11-1 -t- -Oit 



Zinc 91 -j- l-92< 



Thallium 214— -lit 



Silver 250-1- 1-I5t 



Gold 254 + l-Zlt 



Copper 276 4- l-22i! 



Cadmium 285-1- 3-89< 



Antimony 3,558 -f- 14-5< 



14.— A PECULIAR THERMO-ELECTRIC EFFECT. 



£>/ W. RUEY STEELE, M.A. 



