556 Proceedings of the Royal Society 
of his pistons of zinc, his results must be looked upon as 
questionable. 
While in Professor Beetz’ comparison his fulfilment of the first 
condition is not without doubt, his fulfilment of the second is 
certainly not faultless. He forgets the certainty of error arising 
from the use of different standards of measurement, as well as 
the certainty of still greater error from the use of different vessels 
for holding the electrolyte. He recognises, however, the necessity 
of knowing that we worked with the same substances, and this 
fact he proves in a somewhat extraordinary way. His argument 
takes the form of a hypothetical syllogism : — If we used the same 
substances, both methods must have indicated the same solution as 
that of maximum conductivity. Now both methods have done so 
(this itself was only approximately the case). Ergo , we used the 
same substances. The fallacy is evident. He has mixed up what 
the logicians call the modus yonens with the modus tollens , and 
forgotten that a conclusion can be drawn only from a denied, 
never from an affirmed “ consequent.” That Professor Beetz 
intended the “major premise” as we have given it, is evident, 
from the fact that, while he could reasonably expect its admission 
from his readers, he could not expect them to grant the converse, 
viz., that if both he and we had indicated the same solution as 
that of maximum conductivity, we must have used the sanie sub- 
stances. Such an assumption would make his syllogism correct. 
But it neglects what the syllogism itself, according to the first 
version, neglects, viz., the fact of the possible plurality of causes. 
While the method which we used cannot, by Professor Beetz’ 
argument, be proved faulty, the results which we published might 
thus be shown to be unreliable. For that purpose it would be 
necessary that various methods of acknowledged approximate 
accuracy should give results approximately the same, and differing 
widely from ours. Professor Beetz thinks this has been done. 
“ Kohlrausch and Nippoldt have shown how close is the agreement 
between the results which they, Paalzow, and I have obtained in 
three quite different ways. The agreement between their measure- 
ments of zinc- vitriol solutions and mine, and between their 
measurements of dilute sulphuric acid and Paalzow’s, is perfectly 
satisfactory ” One would understand from these sentences that 
