this
would swamp the candidate: but the other two subjects are only to affect
the result collectively, by the amount of knowledge shown, the two being
reckoned of equal value. Here I should add _A_'s German and Italian
marks together, and multiply by his French mark.

But I need not go on: the problem may evidently be set with many varying
conditions, each requiring its own method of solution. The Problem in
Knot VI. was meant to belong to variety (_a_), and to make this clear, I
inserted the following passage:

"Usually the competitors differ in one point only. Thus, last year, Fifi
and Gogo made the same number of scarves in the trial week, and they
were equally light; but Fifi's were twice as warm as Gogo's, and she was
pronounced twice as good."

What I have said will suffice, I hope, as an answer to BALBUS, who holds
that (_a_) and (_c_) are the only possible varieties of the problem, and
that to say "We cannot use addition, therefore we must be intended to
use multiplication," is "no more illogical than, from knowledge that one
was not born in the night, to infer that he was born in the daytime";
and also to FIFEE, who says "I think a little more consideration will
show you that our 'error of _adding_ the proportional numbers together
for each candidate instead of _multiplying_' is no error at all." Why,
even if addition _had_ been the right method to use, not one of the
writers (I speak from memory) showed any consciousness of the necessity
of fixing a "unit" for each subject. "No error at all!" They were
positively steeped in error!

One correspondent (I do not name him, as the communication is not quite
friendly in tone) writes thus:--"I wish to add, very respectfully, that
I think it would be in better taste if you were to abstain from the very
trenchant expressions which you are accustomed to indulge in when
criticising the answer. That such a tone must not be" ("be not"?)
"agreeable to the persons concerned who have made mistakes may possibly
have no great weight with you, but I hope you will feel that it would be
as well not to employ it, _unless you are quite certain of being correct
yourself_." The only instances the writer gives of the "trenchant
expressions" are "hapless" and "malefactors." I beg to assure him (and
any others who may need the assurance: I trust there are none) that all
such words have been used in jest, and with no idea that they could
possibly annoy any one, and that I sincerely re