Aunt Judy was quite aware of these facts, and she had accordingly laid down several rules, and given several instructions to prevent the usual catastrophe; and all went very smoothly at first in consequence.  The little ones went out all hilarity and delight, and divided the tools with considerable show of justice, while Aunt Judy nodded to them approvingly out of her window, and then settled down to an interesting sum in that most peculiar of all arithmetical rules, “The Rule of False,” the principle of which is, that out of two errors, made by yourself from two wrong guesses, you arrive at a discovery of the truth!

When Aunt Judy first caught sight of this rule, a few days before, at the end of an old summing-book, it struck her fancy at once.  The principle of it was capable of a much more general application than to the “Rule of False,” and she amused herself by studying it up.

It is, no doubt, a clumsy substitute for algebra; but young folks who have not learnt algebra, will find it a very entertaining method of making out all such sums as the following old puzzler, over which Aunt Judy was now poring: 

“There is a certain fish, whose head is 9 inches in length, his tail as long as his head and half of his back, and his back as long as both head and tail together.  Query, the length of the fish?”

But Aunt Judy was not left long in peace with her fish.  While she was in the thick of “suppositions” and “errors,” a tap came at the window.

“Aunt Judy!”

“Stop!” was the answer; and the hand of the speaker went up, with the slate-pencil in it, enforcing silence while she pursued her calculations.

“Say, back 42 inches; then tail (half back) 21, and head given, 9, that’s 30, and 30 and 9, 39 back.—­Won’t do!  Second error:  three inches—­What’s the matter, No. 6?  You surely have not begun to quarrel already?”

“Oh, no,” answered No. 6, with her nose flattened against the window-pane.  “But please, Aunt Judy, No. 8 won’t have the oyster-shell trimming round his garden any longer, he says; he says it looks so rubbishy.  But as my garden joins his down the middle, if he takes away the oyster-shells all round his, then one of my sides—­the one in the middle, I mean—­will be left bare, don’t you see? and I want to keep the oyster-shells all round may garden, because mamma says there are still some zoophytes upon them.  So how is it to be?”

What a perplexity!  The fish with his nine-inch head, and his tail as long as his head and half of his back, was a mere nothing to it.

Aunt Judy threw open the window.

“My dear No. 6,” answered she, “yours is the great boundary-line question about which nations never do agree, but go squabbling on till some one has to give way first.  There is but one plan for settling it, and that is, for each of you to give up a piece of your gardens to make a road to run between.  Now if you’ll both give way at once, and consent to this, I will come out to you myself, and leave my fish till the evening.  It’s much too fine to stay in doors, I feel; and I can give you all something real to do.”