" Albert Smith, in one of his amusing novels, describes a woman who was convinced that she suffered from ' cob- wigs on the brain.* This may be a very rare complaint, but in a more metaphorical sense, many of us are very apt to suffer from mental cobwebs, and there is nothing equal to the solving of puzzles and problems for sweeping them away. The solutions to only part of the problems are given. Zerr, Philadelphia, Pa., for critically reading the manuscript. How soon will one be four times the length of the other ? How many calves at .50, sheep at .50, and lambs at $ .60 per head, can be bought for $ 100, the total number bought being 100 ? his estate, and the remain- ing I to ^i S'SOrr, if'SL4ch siie^ji'ld" be ^born ; but | of it to the wife and the other i to the daughter, if such should be born. A room is 30 feet long, 12 feet wide, and 12 feet high. Between 2 and 3 o'clock, I mistook the minute hand for the hour hand, and consequently thought the time 55 min- utes earlier than it was. The area of the frame is \ of the whole area, or J of the area inside the frame. He sways back and forth, each time going ^ as far as he came.
On account of the vari- ous helps placed in this book, it will serve as a handbook of mathematics to both teachers and pupils. It is hoped that this small volume may produce higher and more noble results in awakening a real love and interest among the great body of teachers and students for the study of math- ematics, "the oldest and the noblest, the grandest and the most profound, of all sciences." SAMUEL I. 4.* The area of a rectangular field is 30 acres, and its diag- onal is 100 rods. 5.* Suppose two candles, one of which will burn in 4 hours and the other in 6 hours, are lighted at once. A slate including the frame is 9 inches wide and 12 inches long. If 6 acres of grass, together with what grows on the 6 acres during the time of grazing, keep 16 oxen 12 weeks, and 9 acres keep 26 oxen 9 weeks, how many oxen will 15 acres keep 10 weeks, the grass growing uniformly all the time ? A boy on a sled at the top of a hill 200 feet long, slides down and runs half as far up another hill. 30.* By cutting from a cubical block enough to make each dimension 2 inches shorter it is found that its solidity has been decreased 39,368 cubic inches.
The rules of Mensuration and Short Methods have been included because of their usefulness. Any correction or suggestion relating to these problems and solutions will be most thankfully received. How long was tlie part of the tree that was broken over ? How many acres does a square tract of land contain, which sells for an acre, and is paid for by the number of silver dollars that will lie upon its boundary ? What must be the diam- 4 MATHEMATICAL WEINKLES eter of 8 smaller balls, which, will touch this ball and the faces of the given cube ? At what time between 3 and 4 o'clock is the minute hand the same distance from 8 as the hour hand is from 12 ?
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