A Large and Small Wheel

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We have received a letter from a brother editor in Muncy, Pa., stating that a mathematical question had been mooted in that place, which caused more excitement than the general election. The question is this, "Take two wheels of six feet in diameter, and one of three feet, and secure them fast on an axle— putting the small wheel in the centre of the other two, and then make three tracks for them to run upon, elevating the centre track to the small wheel, so that all will have an equal and proper bearing on the three several tracks to revolve on the same axle ; will they revolve alike m This question, he says, has been referred to him for solution, and his opinion is, that " wheels made fast on the same shaft will all revolve alike." This decision has been contradicted by others, who assert that, " although the three wheels are fixed on the same axis, the small one must slide part of the time, while the large ones revolve." He sends the question to us to give the why and wherefore. We have a great number of such presented, but we seldom do anything more than look them over, because such questions must necessarily take a great deal of time for examination—more than we have to give away, but as this comes from a brother chip, we will present it clearly. The three wheels will revolve in the same time, and the small one will not slide. The circumference of each large wheel is 6X3'14159 =18-84954, that of the small wheel is 3X3' 14159=9.42477. One revolution of the large wheels will describe a straight line On the track of 18'84954 feet, while one revolution will make the small wheel describe a straight line on its track of 9'42477. If the small wheel slides, and yet makes one full revolution, it must describe a line of greater length than this. Well, the question is now put upon those who dispute the decision of our correspondent, to prove how much it slides.— This is altogether a different question from that of the power required to propel wheels of different sizes, and their vis viva.

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