( 169 ) 
tity of observations at our disposal, this is of course the case in a 
much higher degree for non-aqueous solutions. 
It is certain that in general the results obtained by the deter- 
mination of the conductivity, do not agree with those found by a 
non-electric method, but the question is, what conclusions we have 
to draw from this. 
Have we to conclude from what precedes, that the conductivity 
does not always indicate the degree of dissociation, or must we say 
that determinations of the molecular weight in sro which are 
not exceedingly diluted, do not always give information about the 
degree of dissociation ? 
It seems to me that there is more to be said in favour of the 
Jatter conclusion and that the results obtained indicate that in not 
very much diluted solutions ions may oecur at the same time with 
products of polymerization or association and so may be in equilibrium 
with them. 
Before the incorrectness of this supposition has been conclusively 
proved, we should not reject the dissociation theory of ARRHENIUS, 
which has rendered so many and such important services to che- 
mical science. 
Mathematics. — „On the Theory of the Biquadratic Rest’. By 
Prof. LrOPOLD GEGENBAUER (extract of a communication to 
Prof. JAN DE VRIES). 
The way followed in the various textbooks of the theory of 
numbers and even in most lectures on this subject for the general- 
Bike Oe zn; YAN Se ae : m 
isation of the quadratic (=), cubic =| and biquadratic (En) 
Mu Nn n 
restcharacters, explained at first only for prime denominators, seems 
to make the introduction of the generalised symbol appear rather 
arbitrary; hence it does not satisfy the thinking student. The symbol 
referred to is namely defined either as was already done by JAcosi 
by the equation 
DD ren EL] er (ENE) 
that is, by assuming the existence of the theorem of multiplication 
for the denominator (e.g. Dirrcnver, „Vorlesungen über Zahlen- 
