ve "_I_
called yesterday." In short, either of two contradictories disproves the
other: and the moral is that, since a particular proposition is much
more easily proved than a universal one, it is the wisest course, in
arguing with a Lady, to limit one's _own_ assertions to "particulars,"
and leave _her_ to prove the "universal" contradictory, if she can. You
will thus generally secure a _logical_ victory: a _practical_ victory is
not to be hoped for, since she can always fall back upon the crushing
remark "_that_ has nothing to do with it!"--a move for which Man has not
yet discovered any satisfactory answer. Now let us return to BALBUS.)
Here is my "particular negative," on which to test his rule. Suppose the
two recorded luncheons to have been "2 buns, one queen-cake, 2
sausage-rolls, and a bottle of Zoedone: total, one-and-ninepence," and
"one bun, 2 queen-cakes, a sausage-roll, and a bottle of Zoedone: total,
one-and-fourpence." And suppose Clara's unknown luncheon to have been "3
buns, one queen-cake, one sausage-roll, and 2 bottles of Zoedone:" while
the two little sisters had been indulging in "8 buns, 4 queen-cakes, 2
sausage-rolls, and 6 bottles of Zoedone." (Poor souls, how thirsty they
must have been!) If BALBUS will kindly try this by his principle of "two
assumptions," first assuming that a bun is 1_d._ and a queen-cake 2_d._,
and then that a bun is 3_d._ and a queen-cake 3_d._, he will bring out
the other two luncheons, on each assumption, as "one-and-nine-pence" and
"four-and-ten-pence" respectively, which harmony of results, he will
say, "shows that the answers are correct." And yet, as a matter of fact,
the buns were 2_d._ each, the queen-cakes 3_d._, the sausage-rolls
6_d._, and the Zoedone 2_d._ a bottle: so that Clara's third luncheon
had cost one-and-sevenpence, and her thirsty friends had spent
four-and-fourpence!

Another remark of BALBUS I will quote and discuss: for I think that it
also may yield a moral for some of my readers. He says "it is the same
thing in substance whether in solving this problem we use words and call
it Arithmetic, or use letters and signs and call it Algebra." Now this
does not appear to me a correct description of the two methods: the
Arithmetical method is that of "synthesis" only; it goes from one known
fact to another, till it reaches its goal: whereas the Algebraical
method is that of "analysis": it begins with the goal, symbolically
represented, and so goes backwar