(592) 
The question now arises whether it will be possible to explain 
all observations in the domain of thermo-electricity by means of 
suitable assumptions concerning the number of free electrons. In order 
to form an opinion on this point, I shall suppose the Peurier-effect 
to be known, at one definite temperature 7, for all combinations 
of some standard metal with other metals and the THomson-effect to 
have been measured in all metals at all temperatures. Then, after 
having chosen arbitrarily the number N, of free electrons in the 
standard metal at 7, we may deduce from (48) the corresponding 
values for the other conductors, and the equation (44) combined with 
(13) and (14), will serve to determine, for all metals, the value of 
N at any temperature we like. Now, the numbers obtained in this 
way, all of which contain N, as an indeterminate factor, will suffice 
to account for all other thermo-electric phenomena, at least if we 
take for granted that these phenomena obey the laws deduced from 
thermodynamics. Indeed, these laws leading to the relation 
My, 17 + Wy, za + Mur = 9, 
similar to (47), the values of V we have assumed will account not 
only for the Perrwr-effect at the temperature 7, for all metals 
combined with the standard metal, but also for the effect, at the 
same temperature, for any combination. Finally, we see from (45) 
that the value of 11/77 at any temperature may be found from that 
corresponding to 7, if we know the THomson-effeect for all inter- 
mediate temperatures and from (46) that the values of the electro- 
motive force are determined by those of JI. 
There is but one difficulty that might arise in this comparison of 
theory with experimental results; it might be that the assumptions 
we should have to make concerning the numbers NV would prove 
incompatible with theoretical considerations of one kind or another 
about the causes which determine the number of free electrons. 
As to the conductivities for heat and electricity, it would always 
be possible to obtain the right values from (24) and (27), provided 
only we make appropriate assumptions concerning the length / of 
the free path between two encounters *). 
it must be noticed, however, that, whatever be the value of this 
. ; k 
length, the foregoing theory requires that the ratio pn shall be the 
1) If the electric conductivity were inversely proportional to the absolute tempe- 
rature, as it is approximately for some metals, and if we might neglect the varia- 
tions of N, the formula (24) would require that 7 is inversely proportional to 
VT. 1 am unable to explain why MN should vary in this way. 
