310 Proceedings of the Royal Society 
a factor. But it was not till the experiments in my Laboratory 
had been carried on for some months that I was referred by 
Thomson 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 = b (t - t 2 ) + c (t* - tf) + . . . 
where t i and t 2 are temperatures as shown by the ordinary mercurial 
thermometer. 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 
Le Roux has called “ l’efifet Thomson,” which is indispensable to 
the explanation of the observed phenomena. 
All the curves plotted by Messrs May and Straker, 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 dif- 
ferent 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 cir- 
cuit at the hotter parts, the deviations of the mercury thermometers 
from absolute temperature, and the non-correction of the indication 
of the thermometers for the long column of mercury not immersed 
in the hot oil round the junction. 
To settle the question rigorously, I have been for some time ex- 
