
TO A THERMO-ELECTRIC DIAGRAM. 127 
temperatures are the abscisse; the ordinates being parallel to the axis of the 
curve. 
“The electro-motive force in a circuit whose junctions are at absolute tem- 
peratures ¢ and 7 is then represented by 
i Il , 2 iD} 
E=J U oat = 3 (A, — k,)[ 20, (é it) ar (¢ a, t”)] 
t+t’ 
= (t, — bye 0) [4 —"F 
This, of course, is again the equation of a parabola. That ¢ — ?’ is a factor of 
E has long been known, and Tomson has given the results of many experi- 
: t+? . : : 
ments tending to show that ¢, — aa is also a factor. But it was not till the 
experiments in my Laboratory had been carried on for some months that I was 
referred by THomMsSoN to a paper by AvENARIUS (Pogg. Ann. 119), in which it is 
experimentally proved (partly in contradiction of an assertion of BECQUEREL) 
that in a series of five different thermo-electric circuits the electro-motive force 
can be very accurately expressed by two terms of the assumed series 
E=6(4—4) + ¢(é?—7,”) + 
where #, and #, are temperatures as shown by the ordinary mercurial thermo- 
meter. It follows from this that (neglecting the difference between absolute 
temperatures and those given by the mercurial thermometer) E has no other 
variable factor than those above given. 
“Curiously enough, AVENARIUS, whose paper seems to have been written 
mainly for the purpose of attempting to explain (by the consideration merely 
of the effect of heat on electricity of contact of two metals) the production of 
thermo-electric currents, does not allude to the fact that the above equation 
represents a parabola. In fact he gives several figures, in all of which it is 
represented as a very accurately drawn semicircle. He makes no application 
of his empirical formula to the determination of the amount of the Peltier effect, 
nor does he seem to recognise the existence of what Lz Roux has called ‘effet 
Thomson,’ which is indispensable to the explanation of the observed phenomena. 
“ All the curves plotted by Messrs May and Srraxer, which were derived 
from iron, copper, and platinum alone, as well as my own, which included 
cadmium, zinc, tin, lead, brass, silver, and various other substances (sometimes 
arranged with a double arc of two different metals connecting the hot and cold 
junctions) were excellent parabolas. When the temperatures were very high, 
the parabola was slightly steeper on the hotter than on the colder side. This, 
however, was a deviation of very small amount, and quite within the limits of 
error introduced by the altered resistance of the circuit at the hotter parts, the 
deviations of the mercury thermometers from absolute temperature, and the non- 

