to fulfil, or renew that menace. So, if Bay State will so far oblige us as to consider himself demolished, guillotined, axed, and hatcheted by our neglect, we will let him pass into the hands of R. W. R. SYRACUSE, Nov. 20, 1855. MY DEAR MR. MERRY:-I have just returned from a visit to New York, and I find that my Museum is waiting for me, as pleasant and enter tne unintellectual subscribers to old Olympus, We BOSTON, Nov. 19th, 1855. DEAR MR. MERRY:-You don't know how frightened I was-and still am-on taking up the last "Museum," to find in it that terrible threat, made doubly so by the mystery and hidden meaning that enveloped it, as well as by the portentous shake of the head, which, I know, must have accompanied the writing of those words! Why didn't you guillotine, (I "axe" your pardon,) "hatchet" me at once? As it is, I shall be kept a whole month in suspense, thinking of nothing but sharp blades and revolving grindstones! You are quite right about guessing after election, it's always the safest and surest way. But I hardly hink that yours ought fairly to be considered a "guess. "Why, Mr. Merry, I thought that was a fixed fact. When a man's native hills reject him with scorn, there's precious little hope of preferment for that unfortunate from the nation at large. Since X. wants to know what kind of a "stump puller" was used by Willie Coleman in extracting that root, I think it must be a near relation to the one, which, applied to a tooth, used to draw out the skeleton of the body completely! Yours, truly, BAY STATE. I am very much amused and astonished, after the ludicrous amount of effort that has been put forth, not a single method of working the problem has been given, except my own (sneered at as it was), which will stand the test of examination. With hardly a single exception, the demonstrations so far handed in are those which I had tried, and, in my simplicity, rejected as unworthy the scholar. I had yet to learn that black-eyed Mary and Willie Coleman, the chief stars of the Museum constellation, rose superior to all rules, in their original mathematics. E. P. Shaw factors his second equation wrong. He makes x + xy 6 into x: 1+y:: 2 : 3, when the proportion, if he had factored properly, would be x: 2:: 8:1xy. This will produce a very different result. The answer comes right, only because of the interchangeable value of x and y, which have brought him through all the erroneous operations to a correct result. To examine these methods we should try them by strict algebraic rules, and not presume them to be right because the answers are. G. H. B. has solved the question by a rule, which begs the whole question, and involves the very condition of the problem. Ilis solution, in my opinion, is not complete without a demonstration of his rule. And black-eyed Mary, from whom we all expected so much, has failed too. She produces an equation with 0 for its right-hand member. So far so good. She also factors the left member of this equation, and says that one of the factors must be 0. That all will agree to. But thereupon she assumes that y-2 is that one. Now, what right has she to say that this is 9, any more than (y+4y2 x y — 14) the other factor? It seems to me that nothing has been advanced in the course of this discussion inore worthy the name of "guess-work" than this. 1 firmly believe, and I have proved to myself, and to my own satisfaction, that there is no way of escaping a biquadratic equation in the solution of this problem, I may be over-bold in thus attacking everybody, but I have enough of the Young America spirit not to be afraid with right on my side, and I think a careful examination will bear me out. We said next month, did we? Well, we are so overbearingly good-natured, that we forgot all about it, and December did not remind us of it. And now, the old year being defunct, and everybody so busy with good wishes, There is pluck for you. And we like it. smiling faces, and sweet presents, we don't R. W. R. is ahost-a Real Witty Reasoner—a think it would be becoming or appropriate, | Right Worshipful Rabbi. Syracuse stock is up. Black-eyes and Greenpoint must look to it, and G. H. B. and E. P. S. must bestir themselves, or they will all be hors de combat before they are aware. NEW YORK, Nov. 24, 1855. MR. MERRY:-Although I have retired from the puzzle contest, I still have a lively interest in the efforts of the remaining competitors, and hope the vexed question will be speedily decided. To further this end, I herewith send you three solutions, the work of a friend of mine, which you may dispose of as you think best. Yours, truly, WILLIE H. COLEMAN. 1st. x2+ y2=8. Transposing the x in the lower x+xy-6. equation, double the equation and both add it to, and subtract it from, the upper equation, which will give two equations, whose first members will be perfect squares, giving the sum and difference of x and y. Add and subtract the equations last found, and multiply the results together, which frees from radical quantities and gives the value of x y. The value of and afterwards of y is easily obtained from the lower equation. x+y= 6 12 x y =20 x2 + 2 x y + y2: 2 x y + y2 12. = 2 x x+y=20 x-y=√2x 2x= 20 -2x+ 2 x 4 2 x Our mathematical critics are very sharp eyed, Willie, as well as black-eyed. We are 4 afraid they will not be satisfied with all that √2x-4 your friend has done. We pass it over for 2x+2x-4= 16 their inspection. 2nd. - 2 x x2 + y2 = 8 (1) x+xy = 6 (2) xy= 6 x (2) 12-2x (3) To (1) add (3) x2 + 2 x y + y2=20 Extr. root Fr.(1) sub.(3) x2 Extract root x x+y=√20 - 2x - 2 x (4) - 2 x + y2 =2x y= √2x 4 BOSTON, Nov. 23, 1855. MR. HATCHET:-I thought that mathematics was one of the exact sciences, and that algebra furnished the most exact methods of working out its problems. But, from the great ado which our principal scholars are making, and have made since February last, I should think there was nothing exact about it, unless this problem may be called an x-act. It certainly is not a wise one, though there are y's all over it. But it exacts a large space in the Chat. HARRY. Yours, respectfully, Impatient!-hey-tired of the conflict? Well, if that is the case, we must try to bring it to a close in the next number, and that will make a full year of it, since the problem was given out. The discussion did not com. mence till July, however, and did not grow warm till November, when the weather began | one of our little company is, at this moment, to grow cool. BROOKLYN, Nov. 28th, 1855. DEAR UNCLE HIRAM:-About that problem, it does seem to me that any person, having half an eye open, might solve it without all the fuss and parade of letters we have had in the Museum. The problem is x2+y2=8 x + xy-6. Now it is plain that no two squares can go to make up 8 but 4 and 4. Therefore x and y must both be 2. And that is the whole of it. Where's the use of all those letters and squares and plusses. It is very much as if a man should go to a house, and find the door wide open, and, instead of walking right in, go round the back side, climb up the lightning rod, and creep down the chimney. Them's my sentiments. With great respect, Yours truly, HENRY STREET. There is more common sense than Algebra in Henry street, to whom we will only suggest that to every result there is a right and a wrong way. In this case, the Algebraists find the door locked, and each one is trying to open it with his own key, while Henry street is for jumping in at the open window, or letting himself down through the scuttle, just as Willie Coleman did in the March number, page 93. open standing over a fire, cooking up "suthin good" -suthin which I shall help to disappear, as soon as I have finished this hasty epistle. About a mile north of our cabin, is a beautiful little lake; and on the banks of it, all "solitary and alone," lives an old hunter and trapper, who goes by the name of Uncle Ben. He is a perfect giant in stature, and, though well advanced in years, is seemingly as hearty and strong as ever, He still follows the chase for a livelihood, and we frequently go over to his cabin in the evening, and hear, him "spin yarns" about his younger days, and the many exciting scenes he has witnessed. He has a canoe, or "dug-out," and we frequently borrow it, to skim over the lake. Uncle Ben has a dog, seemingly as old as himself, and the quaint looking pair go out into the thick woods every day to hunt. The other day, we saw Uncle Ben kill a deer; and a wild and exciting scene it was, I assure you. The noble animal was dashing along, a little south of Uncle Ben's cabin, while he was standing in his door. He instantly raised his long rifle, which he keeps always ready, and taking deliberate aim, shot the deer through the head, and brought him to the ground. He then skinned him, and after taking all that he wanted for his own use, left the remainder to the hungry wolves, who prowl every night around the spot. Ben keeps all the skins he gets, and sells them in the "settlements." He has a large pile of them in the cabin now, and they make a splendid bed. But the boys are calling me to supper, and if I do not go soon, I shall not get any; so I shall close this letter here. We leave for home in a day or two, and shall drop this letter in some Post-office, on our way home. With love for the Museum, I remain its friend, JACK WILSON. Fine sport, indeed, young rovers. Uncle Hiram would like to have joined you. When you go again, tip him the wink, and he will be there. BRIDGEWATER, November 15, 1855. MR. MERRY, DEAR SIR:-Agreeably to your request, I send you the Answer to No. 298. Cimeter are BACKWOODS, GENESEE Co., N. Y., Nov. 1, 1855. DEAR ROBERT MERRY:-I am writing this letter to you on a smooth piece of bark, laid across an old stump, while I am seated on a fallen log, directly in front of a little shanty, which is, for the time being, our home. We "Albany Boys," and are spending a long Cimatar vacation in these glorious old woods. You may think queerly of our notion, yet I assure you we have "prime fun." Cimetar Cimmetur Cymatir Cymmatur Cimetir Cimmiter Cymatur Simeter Cimetur Cimmitar Cymatar Simetir Cimiter Cimmitur Cymmeter Simetar Cymmetar Simetur Cymmetir Simiter Cymmetur Simitir Cymetir Cymmiter Simitur Cymetur Cymmitar Simitar Cimatir Cymiter Cymmitir Simater Cimatur Cymitar Cymmitur Simatir Cimmeter Cymitur Cymmater Simatar We have a neat little cabin, built of bark, and Cimmetar Cymitir Cymmatar Simatur Symitur Scimetir Scimmitur Scymiter Symater Scymetar Symatir Scimetur Symatar Scimater Scimmatar Scymitar Scimmatur Scymitur Symmeter Scimatir Scymmeter Scymitir Symmetir Scimatur Scymmetir Scymitar Symmetar Scimiter Scymmetar Scymatir Symmetur Scimitir Scymmetur Scymater Symmiter Scimitar Scymmiter Scymatur. Symmitar Scimitur Scymmitir 1. Charade. 2. When does the tongue assume the funotions of the teeth? 3. My first is company, my second is without company, and my third calls company. 4. When is a fish crazy? 5. An emblem of stupidity, My FIRST in forests found; Though fastened to the ground. Or, perhaps, it makes a blaze. Is good, or bad, or gay; Is dull or bright, to suit all minds, The patient seaman keeps with care my WHOLE, N. B. No. 2. We are obliged to cut short our questions and puzzles-for want of room. We have a large number of letters on hand 331. When they chatter. L. A. Bent and for the Chat, but are so crowded with other Frank Eugene. 334. Love. L. A. Bent and Bay State. 335. Because it is always in doubt. Frank E. Because it is in the midst of doubt. A. C. W. 336. Sebastopol is taken. Frank E. matter, that we must lay them over till next month, when we will bring all up square, and make a Chat long enough for every one to put in his word. Meanwhile, we will just say, in 338. Governor Reeder. James and A. C. W. parting, that "Gilbert Go-ahead," and the Governor Gardner. L. A. Bent. 340. Buffalo. James. 341. Iowa. L. A. Bent, Bay State, J. E. C. 342. When it is an alley. A. C. W. 342. When he is a poet. W. C. N. B. There were some sad mistakes in the Riddle on page 183. In the 7th line shy should be sly. In the 17th line Evea should be Eve. In the 21st, Mary should be Margaret. "Balloon Travels" have been printed in two handsome volumes, and are published by J. C. Derby, of New York. They are handsomely illustrated, and will no doubt be welcome to all our young readers, though they are already familiar with some parts of the story. In the books, as now published, there is much new matter, that was not given in the Museum, and all of the most entertaining character. |